{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T18:01:13Z","timestamp":1775671273647,"version":"3.50.1"},"reference-count":62,"publisher":"EDP Sciences","issue":"6","license":[{"start":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T00:00:00Z","timestamp":1660262400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ESAIM: M2AN"],"accepted":{"date-parts":[[2022,6,24]]},"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:p>We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic image<jats:italic>\u03d5<\/jats:italic>(\u2202\u03a9) of a reference set \u2202\u03a9 and we present some real analyticity results for the dependence upon the map<jats:italic>\u03d5<\/jats:italic>. Then we introduce a perforated domain \u03a9(<jats:italic>\u03b5<\/jats:italic>) with a small hole of size<jats:italic>\u03b5<\/jats:italic>and we compute power series expansions that describe the layer potentials on \u2202\u03a9(<jats:italic>\u03b5<\/jats:italic>) when the parameter<jats:italic>\u03b5<\/jats:italic>approximates the degenerate value<jats:italic>\u03b5<\/jats:italic>\u00a0=\u00a00.<\/jats:p>","DOI":"10.1051\/m2an\/2022057","type":"journal-article","created":{"date-parts":[[2022,6,27]],"date-time":"2022-06-27T18:54:49Z","timestamp":1656356089000},"page":"1889-1910","source":"Crossref","is-referenced-by-count":6,"title":["Shape analyticity and singular perturbations for layer potential operators"],"prefix":"10.1051","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5519-3327","authenticated-orcid":false,"given":"Matteo","family":"Dalla Riva","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0765-001X","authenticated-orcid":false,"given":"Paolo","family":"Luzzini","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7366-5124","authenticated-orcid":false,"given":"Paolo","family":"Musolino","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2022,8,12]]},"reference":[{"key":"R1","unstructured":"Ammari H. and Kang H., Polarization and Moment Tensors. Vol. 162 of Applied Mathematical Sciences. Springer, New York (2007)."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Ammari H., Kang H. and Lee H., Layer Potential Techniques in Spectral Analysis. Mathematical Surveys and Monographs. Vol. 153. American Mathematical Society, Providence, RI (2009).","DOI":"10.1090\/surv\/153\/10"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"Ammari H., Fitzpatrick B., Kang H., Ruiz M., Yu S. and Zhang H., Mathematical and Computational Methods in Photonics and Phononics. Mathematical Surveys and Monographs. Vol. 235. American Mathematical Society, Providence, RI (2018).","DOI":"10.1090\/surv\/235"},{"key":"R4","doi-asserted-by":"crossref","first-page":"273","DOI":"10.4064\/sm-35-3-273-292","volume":"35","author":"Bochnak","year":"1970","journal-title":"Stud. Math."},{"key":"R5","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1088\/0266-5611\/11\/6\/002","volume":"11","author":"Charalambopoulos","year":"1995","journal-title":"Inverse Prob."},{"key":"R6","doi-asserted-by":"crossref","first-page":"1720","DOI":"10.1137\/16M1099406","volume":"50","author":"Cohen","year":"2018","journal-title":"SIAM J. Math. Anal."},{"key":"R7","unstructured":"Coifman R. and Meyer Y., Lavrentiev\u2019s curves and conformal mappings. Institut Mittag-Leffler, Report No. 5. (1983)."},{"key":"R8","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/s00020-012-1954-z","volume":"72","author":"Costabel","year":"2012","journal-title":"Integral Equ. Oper. Theory"},{"key":"R9","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s00020-012-1955-y","volume":"73","author":"Costabel","year":"2012","journal-title":"Integral Equ. Oper. Theory"},{"key":"R10","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s00020-017-2377-7","volume":"88","author":"Costabel","year":"2017","journal-title":"Integral Equ. Oper. Theory"},{"key":"R11","unstructured":"Dalla Riva M., Potential theoretic methods for the analysis of singularly perturbed problems in linearized elasticity. Ph.D. thesis, University of Padova (2008)."},{"key":"R12","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1080\/17476931003628216","volume":"55","author":"Dalla Riva","year":"2010","journal-title":"Complex Var. Elliptic Equ."},{"key":"R13","first-page":"31","volume":"1","author":"Dalla Riva","year":"2010","journal-title":"Eur. Math. J."},{"key":"R14","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1007\/s11785-010-0109-y","volume":"5","author":"Dalla Riva","year":"2011","journal-title":"Complex Anal. Oper. Theory"},{"key":"R15","first-page":"10","volume":"5","author":"Dalla Riva","year":"2010","journal-title":"J. Appl. Funct. Anal."},{"key":"R16","doi-asserted-by":"crossref","first-page":"6337","DOI":"10.1016\/j.jde.2012.03.007","volume":"252","author":"Dalla Riva","year":"2012","journal-title":"J. Differ. Equ."},{"key":"R17","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.jmaa.2014.08.037","volume":"422","author":"Dalla Riva","year":"2015","journal-title":"J. Math. Anal. Appl."},{"key":"R18","doi-asserted-by":"crossref","first-page":"339","DOI":"10.3233\/ASY-151283","volume":"92","author":"Dalla Riva","year":"2015","journal-title":"Asymptotic Anal."},{"key":"R19","doi-asserted-by":"crossref","first-page":"217","DOI":"10.3233\/ASY-181495","volume":"111","author":"Dalla Riva","year":"2019","journal-title":"Asymptotic Anal."},{"key":"R20","doi-asserted-by":"crossref","unstructured":"Dalla Riva M., Lanza de Cristoforis M. and Musolino P., Singularly Perturbed Boundary Value Problems: A Functional Analytic Approach. Springer Nature, Cham (2021).","DOI":"10.1007\/978-3-030-76259-9"},{"key":"R21","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1088\/1361-6420\/ac5eea","volume":"38","author":"Dalla Riva","year":"2022","journal-title":"Inverse Prob."},{"key":"R22","doi-asserted-by":"crossref","unstructured":"Dalla Riva M., Luzzini P., Musolino P. and Pukhtaievych R., Dependence of effective properties upon regular perturbations. In: Mechanics and Physics of Structured Media: Asymptotic and Integral Equations Methods of Leonid Filshtinsky, edited by Andrianov I., Gluzman S. and Mityushev V.. Elsevier (2022) 271\u2013301.","DOI":"10.1016\/B978-0-32-390543-5.00019-0"},{"key":"R23","doi-asserted-by":"crossref","unstructured":"Deimling K., Nonlinear Functional Analysis. Springer-Verlag, Berlin (1985).","DOI":"10.1007\/978-3-662-00547-7"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"Feppon F. and Ammari H., High order topological asymptotics: reconciling layer potentials and compound asymptotic expansions. Multiscale Model. Simul.. Preprint hal-03440755. (2021).","DOI":"10.1137\/21M1461277"},{"key":"R25","doi-asserted-by":"crossref","unstructured":"Feppon F. and Ammari H., Homogenization of sound-absorbing and high-contrast acoustic metamaterials in subcritical regimes. SAM Research Report No. 2021-35. Preprint hal-03372593 (2021).","DOI":"10.1051\/m2an\/2022098"},{"key":"R26","unstructured":"Folland G.B., Introduction to Partial Differential Equations, 2nd edition. Princeton University Press, Princeton, NJ (1995)."},{"key":"R27","unstructured":"Gilbarg D. and Trudinger N.S., Elliptic Partial Differential Equations of Second Order, 2nd edition. Vol. 224 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (1983)."},{"key":"R28","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1137\/S0036139903435413","volume":"65","author":"Haddar","year":"2004","journal-title":"SIAM J. Appl. Math."},{"key":"R29","doi-asserted-by":"crossref","unstructured":"H\u00e1jek P. and Johanis M., Smooth Analysis in Banach Spaces. Vol. 19 of de Gruyter Series in Nonlinear Analysis and Applications. De Gruyter, Berlin (2014).","DOI":"10.1515\/9783110258998"},{"key":"R30","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/s00020-021-02653-5","volume":"93","author":"Henr\u00edquez","year":"2021","journal-title":"Integral Equ. Oper. Theory"},{"key":"R31","first-page":"24","volume":"32","author":"Ivanyshyn Yaman","year":"2016","journal-title":"Inverse Prob."},{"key":"R32","doi-asserted-by":"crossref","first-page":"2229","DOI":"10.1142\/S0218202517500439","volume":"27","author":"Jerez-Hanckes","year":"2017","journal-title":"Math. Models Methods Appl. Sci."},{"key":"R33","doi-asserted-by":"crossref","unstructured":"Kress R., Linear Integral Equations, 3rd edition. Applied Mathematical Sciences. Vol. 82. Springer-Verlag, New York (2014).","DOI":"10.1007\/978-1-4614-9593-2"},{"key":"R34","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1137\/S0036139997332257","volume":"59","author":"Kress","year":"1999","journal-title":"SIAM J. Appl. Math."},{"key":"R35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF03321008","volume":"2","author":"Lanza de Cristoforis","year":"2002","journal-title":"Comput. Methods Funct. Theory"},{"key":"R36","first-page":"851","volume":"50","author":"Lanza de Cristoforis","year":"2005","journal-title":"Complex Var. Theory Appl."},{"key":"R37","first-page":"197","volume":"2","author":"Lanza de Cristoforis","year":"2007","journal-title":"J. Appl. Funct. Anal."},{"key":"R38","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1080\/17476930701485630","volume":"52","author":"Lanza de Cristoforis","year":"2007","journal-title":"Complex Var. Elliptic Equ."},{"key":"R39","first-page":"63","volume":"28","author":"Lanza de Cristoforis","year":"2008","journal-title":"Anal. M\u00fcnchen"},{"key":"R40","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/17476930902999058","volume":"55","author":"Lanza de Cristoforis","year":"2010","journal-title":"Complex Var. Elliptic Equ."},{"key":"R41","first-page":"75","volume":"52","author":"Lanza de Cristoforis","year":"2011","journal-title":"Far East J. Math. Sci. (FJMS)"},{"key":"R42","first-page":"21","volume":"25","author":"Lanza de Cristoforis","year":"2013","journal-title":"J. Integral Equ. Appl."},{"key":"R43","first-page":"363","volume":"11","author":"Lanza de Cristoforis","year":"1999","journal-title":"J. Integral Equ. Appl."},{"key":"R44","first-page":"137","volume":"16","author":"Lanza de Cristoforis","year":"2004","journal-title":"J. Integral Equ. Appl."},{"key":"R45","unstructured":"Lanza de Cristoforis M. and Rossi L., Real analytic dependence of simple and double layer potentials for the Helmholtz equation upon perturbation of the support and of the density. In: Analytic Methods of Analysis and Differential Equations: AMADE 2006. Camb. Sci. Publ, Cambridge (2008) 193\u2013220."},{"key":"R46","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1137\/110834160","volume":"72","author":"Le Lou\u00ebr","year":"2012","journal-title":"SIAM J. Appl. Math."},{"key":"R47","doi-asserted-by":"crossref","first-page":"581","DOI":"10.3934\/nhm.2020015","volume":"15","author":"Luzzini","year":"2020","journal-title":"Netw. Heterog. Media"},{"key":"R48","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1016\/j.jmaa.2019.05.017","volume":"477","author":"Luzzini","year":"2019","journal-title":"J. Math. Anal. Appl."},{"key":"R49","doi-asserted-by":"crossref","unstructured":"Maz\u2019ya V., Nazarov S. and Plamenevskii B., Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Vol. I. Birkh\u00e4user, Basel (2000).","DOI":"10.1007\/978-3-0348-8434-1"},{"key":"R50","doi-asserted-by":"crossref","unstructured":"Maz\u2019ya V., Nazarov S. and Plamenevskii B., Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Vol. II. Birkh\u00e4user, Basel (2000).","DOI":"10.1007\/978-3-0348-8434-1"},{"key":"R51","doi-asserted-by":"crossref","unstructured":"Maz\u2019ya V.G., Movchan A.B. and Nieves M.J., Green\u2019s Kernels and Meso-Scale Approximations in Perforated Domains. Lecture Notes in Mathematics. Vol. 2077. Springer, Berlin (2013).","DOI":"10.1007\/978-3-319-00357-3"},{"key":"R52","doi-asserted-by":"crossref","first-page":"247","DOI":"10.2307\/1968995","volume":"42","author":"Michal","year":"1941","journal-title":"Ann. Math."},{"key":"R53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4064\/sm-134-1-1-33","volume":"134","author":"Mu\u00f1oz","year":"1999","journal-title":"Stud. Math."},{"key":"R54","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1088\/0266-5611\/10\/2\/016","volume":"10","author":"Potthast","year":"1994","journal-title":"Inverse Prob."},{"key":"R55","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1515\/jiip.1996.4.1.67","volume":"4","author":"Potthast","year":"1996","journal-title":"J. Inverse Ill-Posed Probl."},{"key":"R56","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1002\/(SICI)1099-1476(199610)19:15<1157::AID-MMA814>3.0.CO;2-Y","volume":"19","author":"Potthast","year":"1996","journal-title":"Math. Methods Appl. Sci."},{"key":"R57","unstructured":"Prodi G. and Ambrosetti A., Analisi Non Lineare. Editrice Tecnico Scientifica, Pisa (1973)."},{"key":"R58","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s00033-018-0976-z","volume":"69","author":"Pukhtaievych","year":"2018","journal-title":"Z. Angew. Math. Phys."},{"key":"R59","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1007\/BF01174371","volume":"33","author":"Schauder","year":"1931","journal-title":"Math. Z."},{"key":"R60","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1007\/BF01186569","volume":"35","author":"Schauder","year":"1932","journal-title":"Math. Z."},{"key":"R61","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1090\/S0002-9904-1943-07968-2","volume":"49","author":"Taylor","year":"1943","journal-title":"Bull. Am. Math. Soc."},{"key":"R62","doi-asserted-by":"crossref","unstructured":"Valent T., Boundary Value Problems of Finite Elasticity. Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data. Springer Tracts in Natural Philosophy. Vol. 31. Springer-Verlag, New York (1988).","DOI":"10.1007\/978-1-4612-3736-5"}],"container-title":["ESAIM: Mathematical Modelling and Numerical Analysis"],"original-title":[],"link":[{"URL":"https:\/\/www.esaim-m2an.org\/10.1051\/m2an\/2022057\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T20:09:13Z","timestamp":1675973353000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.esaim-m2an.org\/10.1051\/m2an\/2022057"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,12]]},"references-count":62,"journal-issue":{"issue":"6"},"alternative-id":["m2an220046"],"URL":"https:\/\/doi.org\/10.1051\/m2an\/2022057","relation":{},"ISSN":["2822-7840","2804-7214"],"issn-type":[{"value":"2822-7840","type":"print"},{"value":"2804-7214","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,12]]}}}