{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:36:07Z","timestamp":1787319367531,"version":"build-2736575974"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Belgian National Fund for Scientific Research","award":["40006150"],"award-info":[{"award-number":["40006150"]}]},{"name":"OeAD-WTZ","award":["CZ 01\/2021"],"award-info":[{"award-number":["CZ 01\/2021"]}]},{"name":"Istituto Nazionale di Alta Matematica"},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["FW506004"],"award-info":[{"award-number":["FW506004"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["F65"],"award-info":[{"award-number":["F65"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P32788"],"award-info":[{"award-number":["P32788"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["W 1245"],"award-info":[{"award-number":["W 1245"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["I 4354"],"award-info":[{"award-number":["I 4354"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["I 5149"],"award-info":[{"award-number":["I 5149"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2024,2,29]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We consider a class of elliptic and parabolic problems featuring a specific nonlocal operator of fractional Laplacian type, where integration is taken on variable domains. Both elliptic and parabolic problems are proved to be uniquely solvable in the viscosity sense. Moreover, some spectral properties of the elliptic operator are investigated, proving existence and simplicity of the first eigenvalue. Eventually, parabolic solutions are proven to converge to the corresponding limiting elliptic solution in the long-time limit.<\/jats:p>","DOI":"10.1137\/22m1511503","type":"journal-article","created":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T04:46:02Z","timestamp":1704689162000},"page":"336-373","source":"Crossref","is-referenced-by-count":1,"title":["Viscosity Solutions for Nonlocal Equations with Space-Dependent Operators"],"prefix":"10.1137","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0667-233X","authenticated-orcid":true,"given":"Stefano","family":"Buccheri","sequence":"first","affiliation":[{"name":"Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ulisse","family":"Stefanelli","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria, and Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, W\u00e4hringerstrasse 17, A-1090 Vienna, Austria, and Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, via Ferrata 1, I-27100 Pavia, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,1,8]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2017021"},{"key":"ref2","series-title":"Math. Surveys Monogr. 165","volume-title":"Nonlocal Diffusion Problems","author":"Andreu-Vaillo F.","year":"2021"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4755-1"},{"key":"ref4","series-title":"Lecture Notes in Math. 2074","first-page":"49","volume-title":"Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications","author":"Barles G."},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2008.57.3315"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.4171\/jems\/242"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2007.02.007"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.4171\/RMI\/983"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160470105"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.3934\/dcdss.2011.4.1"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.57262\/ade\/1355867725"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s10231-022-01203-z"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2019.11.011"},{"key":"ref14","unstructured":"A. Biswas  and \nM. Modasiya  , Mixed Local-Nonlocal Operators: Maximum Principles, Eigenvalue Problems and Their Applications, preprint, https:\/\/arxiv.org\/abs\/2110.06746, 2021."},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-003-0275-1"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2021.05.005"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2004.05.004"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20274"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-010-0336-4"},{"key":"ref20","unstructured":"H. Chen , \nH. Peng , and \nY. Sun  , On Schr\u00f6dinger Equations Involving the Regional Fractional Laplacian in a Ball with the Zero Boundary Condition, preprint, https:\/\/arxiv.org\/abs\/2211.10554, 2022."},{"key":"ref21","unstructured":"H. Chen  and \nY. Wei  , Liouville Theorems for Elliptic Equations Involving Regional Fractional Laplacian with Order in (0;1\/2], preprint, https:\/\/arxiv.org\/abs\/2007.05775, 2020."},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1992-00266-5"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-012-0576-2"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2015.11.012"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0327-8"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2018.10.046"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530521500329"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"231","DOI":"10.3934\/dcdsb.2018110","volume":"24","author":"Duo S.","year":"2019","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"ref29","series-title":"Lect. Notes Comput. Sci. Eng. 89","first-page":"45","volume-title":"Meshfree Methods for Partial Differential Equations VI","author":"Emmrich E.","year":"2008"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2022.02.040"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/7877"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.06.001"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-005-0031-6"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2014.63.5394"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109009"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2010.59.4128"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-010-0354-2"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.2140\/apde.2017.10.1227"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2007.12.002"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2020003"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2013.06.003"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.5565\/PUBLMAT_60116_01"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1215\/00127094-3476700"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.2140\/apde.2016.9.727"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5096(99)00029-0"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-2156(10)44002-8"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2006.55.2706"},{"key":"ref48","series-title":"Lect. Notes Unione Mat. Ital. 3","volume-title":"An Introduction to Sobolev Spaces and Interpolation Spaces","author":"Tartar L.","year":"2007"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1511503","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:48:05Z","timestamp":1787316485000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1511503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,8]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2,29]]}},"alternative-id":["10.1137\/22M1511503"],"URL":"https:\/\/doi.org\/10.1137\/22m1511503","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,8]]}}}