{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T03:20:23Z","timestamp":1777605623323,"version":"3.51.4"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T00:00:00Z","timestamp":1600473600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T00:00:00Z","timestamp":1600473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000086","name":"Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","award":["1411646"],"award-info":[{"award-number":["1411646"]}],"id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000147","name":"Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["1629026"],"award-info":[{"award-number":["1629026"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007297","name":"Office of Naval Research Global","doi-asserted-by":"publisher","award":["N00014-18-1-2766"],"award-info":[{"award-number":["N00014-18-1-2766"]}],"id":[{"id":"10.13039\/100007297","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014036","name":"Multidisciplinary University Research Initiative","doi-asserted-by":"publisher","award":["FA9550-12-1-0458"],"award-info":[{"award-number":["FA9550-12-1-0458"]}],"id":[{"id":"10.13039\/100014036","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014036","name":"Multidisciplinary University Research Initiative","doi-asserted-by":"publisher","award":["FA9550-16-1-0566"],"award-info":[{"award-number":["FA9550-16-1-0566"]}],"id":[{"id":"10.13039\/100014036","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2020,12]]},"DOI":"10.1007\/s00332-020-09653-6","type":"journal-article","created":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T16:02:27Z","timestamp":1600531347000},"page":"3367-3388","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Bounds on the Energy of a Soft Cubic Ferromagnet with Large Magnetostriction"],"prefix":"10.1007","volume":"30","author":[{"given":"Raghavendra","family":"Venkatraman","sequence":"first","affiliation":[]},{"given":"Vivekanand","family":"Dabade","sequence":"additional","affiliation":[]},{"given":"Richard D.","family":"James","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,19]]},"reference":[{"key":"9653_CR1","volume-title":"Ginzburg\u2013Landau Vortices. Progress in Nonlinear Differential Equations and their Applications","author":"F Bethuel","year":"1994","unstructured":"Bethuel, F., Brezis, H., H\u00e9lein, F.: Ginzburg\u2013Landau Vortices. Progress in Nonlinear Differential Equations and their Applications, vol. 13. Birkh\u00e4user Boston Inc, Boston (1994)"},{"issue":"3","key":"9653_CR2","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1002\/(SICI)1097-0312(199803)51:3<259::AID-CPA3>3.0.CO;2-9","volume":"51","author":"R Choksi","year":"1998","unstructured":"Choksi, R., Kohn, R.V.: Bounds on the micromagnetic energy of a uniaxial ferromagnet. Commun. Pure Appl. Math. 51(3), 259\u2013289 (1998)","journal-title":"Commun. Pure Appl. Math."},{"issue":"1","key":"9653_CR3","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s002200050549","volume":"201","author":"R Choksi","year":"1999","unstructured":"Choksi, R., Kohn, R.V., Otto, F.: Domain branching in uniaxial ferromagnets: a scaling law for the minimum energy. Commun. Math. Phys. 201(1), 61\u201379 (1999)","journal-title":"Commun. Math. Phys."},{"issue":"7552","key":"9653_CR4","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1038\/nature14459","volume":"521","author":"HD Chopra","year":"2015","unstructured":"Chopra, H.D., Wuttig, M.: Non-joulian magnetostriction. Nature 521(7552), 340\u2013343 (2015)","journal-title":"Nature"},{"key":"9653_CR5","first-page":"415","volume":"21","author":"V Dabade","year":"2018","unstructured":"Dabade, V., Venkatraman, R., James, R.D.: Micromagnetics of galfenol. J. Nonlinear Sci. 21, 415\u2013460 (2018)","journal-title":"J. Nonlinear Sci."},{"issue":"2","key":"9653_CR6","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/S0022-5096(01)00050-3","volume":"50","author":"A DeSimone","year":"2002","unstructured":"DeSimone, A., James, R.D.: A constrained theory of magnetoelasticity. J. Mech. Phys. Solids 50(2), 283\u2013320 (2002)","journal-title":"J. Mech. Phys. Solids"},{"key":"9653_CR7","doi-asserted-by":"publisher","first-page":"2983","DOI":"10.1098\/rspa.2001.0846","volume":"457","author":"A DeSimone","year":"2001","unstructured":"DeSimone, A., Kohn, R.V., M\u00fcller, S., Otto, F., Sch\u00e4fer, R.: Two-dimensional modelling of soft ferromagnetic films. Proc. R. Soc. Lond. A. Math. Phys. Eng. Sci. 457, 2983\u20132991 (2001a)","journal-title":"Proc. R. Soc. Lond. A. Math. Phys. Eng. Sci."},{"issue":"4","key":"9653_CR8","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1017\/S030821050000113X","volume":"131","author":"A DeSimone","year":"2001","unstructured":"DeSimone, A., M\u00fcller, S., Kohn, R.V., Otto, F.: A compactness result in the gradient theory of phase transitions. Proc. R. Soc. Edinb. Sect. A 131(4), 833\u2013844 (2001b)","journal-title":"Proc. R. Soc. Edinb. Sect. A"},{"issue":"4","key":"9653_CR9","first-page":"269","volume":"2","author":"A DeSimone","year":"2006","unstructured":"DeSimone, A., Kohn, R.V., M\u00fcller, S., Otto, F., et al.: Recent analytical developments in micromagnetics. Sci. Hysteresis 2(4), 269\u2013381 (2006)","journal-title":"Sci. Hysteresis"},{"issue":"2","key":"9653_CR10","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1002\/cpa.21868","volume":"73","author":"F Ghiraldin","year":"2020","unstructured":"Ghiraldin, F., Lamy, X.: Optimal Besov differentiability for entropy solutions of the Eikonal equation. Commun. Pure Appl. Math. 73(2), 317\u2013349 (2020)","journal-title":"Commun. Pure Appl. Math."},{"issue":"4","key":"9653_CR11","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/s101140100136","volume":"17","author":"FB Hang","year":"2001","unstructured":"Hang, F.B., Lin, F.H.: Static theory for planar ferromagnets and antiferromagnets. Acta Math. Sin. (Engl. Ser.) 17(4), 541\u2013580 (2001)","journal-title":"Acta Math. Sin. (Engl. Ser.)"},{"key":"9653_CR12","volume-title":"Magnetic Domains: The Analysis of Magnetic Microstructures","author":"A Hubert","year":"2008","unstructured":"Hubert, A., Sch\u00e4fer, R.: Magnetic Domains: The Analysis of Magnetic Microstructures. Springer, Berlin (2008)"},{"issue":"1","key":"9653_CR13","first-page":"187","volume":"1","author":"P-E Jabin","year":"2002","unstructured":"Jabin, P.-E., Otto, F., Perthame, B.: Line-energy Ginzburg\u2013Landau models: zero-energy states. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 1(1), 187\u2013202 (2002)","journal-title":"Annali della Scuola Normale Superiore di Pisa-Classe di Scienze"},{"issue":"5","key":"9653_CR14","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1080\/01418619808214252","volume":"77","author":"RD James","year":"1998","unstructured":"James, R.D., Wuttig, M.: Magnetostriction of martensite. Philos. Mag. A 77(5), 1273\u20131299 (1998)","journal-title":"Philos. Mag. A"},{"issue":"6","key":"9653_CR15","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1002\/cpa.21448","volume":"66","author":"H Kn\u00fcpfer","year":"2013","unstructured":"Kn\u00fcpfer, H., Kohn, R.V., Otto, F.: Nucleation barriers for the cubic-to-tetragonal phase transformation. Commun. Pure Appl. Math. 66(6), 867\u2013904 (2013)","journal-title":"Commun. Pure Appl. Math."},{"issue":"3","key":"9653_CR16","first-page":"97","volume":"15","author":"E Lifshitz","year":"1945","unstructured":"Lifshitz, E.: On the magnetic structure of iron. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 15(3), 97\u2013107 (1945)","journal-title":"Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki"},{"issue":"3","key":"9653_CR17","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1051\/m2an\/1981150302371","volume":"15","author":"JA Nitsche","year":"1981","unstructured":"Nitsche, J.A.: On Korn\u2019s second inequality. RAIRO. Analyse num\u00e9rique 15(3), 237\u2013248 (1981)","journal-title":"RAIRO. Analyse num\u00e9rique"},{"key":"9653_CR18","volume-title":"Topics in Fourier Analysis and Function Spaces","author":"H-J Schmeisser","year":"1987","unstructured":"Schmeisser, H.-J., Triebel, H.: Topics in Fourier Analysis and Function Spaces. Wiley, Chichester (1987)"},{"issue":"3","key":"9653_CR19","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/BF00253122","volume":"101","author":"P Sternberg","year":"1988","unstructured":"Sternberg, P.: The effect of a singular perturbation on nonconvex variational problems. Arch. Ration. Mech. Anal. 101(3), 209\u2013260 (1988)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"3","key":"9653_CR20","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s002050100157","volume":"160","author":"A Vasseur","year":"2001","unstructured":"Vasseur, A.: Strong traces for solutions of multidimensional scalar conservation laws. Arch. Ration. Mech. Anal. 160(3), 181\u2013193 (2001)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"9","key":"9653_CR21","doi-asserted-by":"publisher","first-page":"2845","DOI":"10.1016\/j.actamat.2005.03.002","volume":"53","author":"JX Zhang","year":"2005","unstructured":"Zhang, J.X., Chen, L.Q.: Phase-field microelasticity theory and micromagnetic simulations of domain structures in giant magnetostrictive materials. Acta Mater. 53(9), 2845\u20132855 (2005)","journal-title":"Acta Mater."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-020-09653-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-020-09653-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-020-09653-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,19]],"date-time":"2021-09-19T00:44:26Z","timestamp":1632012266000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-020-09653-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,19]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["9653"],"URL":"https:\/\/doi.org\/10.1007\/s00332-020-09653-6","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,19]]},"assertion":[{"value":"13 June 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 September 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 September 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}