{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T04:25:59Z","timestamp":1770438359029,"version":"3.49.0"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2014,1,19]],"date-time":"2014-01-19T00:00:00Z","timestamp":1390089600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Calc. Var."],"published-print":{"date-parts":[[2015,1]]},"DOI":"10.1007\/s00526-013-0705-6","type":"journal-article","created":{"date-parts":[[2014,1,18]],"date-time":"2014-01-18T05:23:41Z","timestamp":1390022621000},"page":"65-93","source":"Crossref","is-referenced-by-count":10,"title":["On the minimizers of calculus of variations problems in Hilbert spaces"],"prefix":"10.1007","volume":"52","author":[{"given":"Diogo","family":"Gomes","sequence":"first","affiliation":[]},{"given":"Levon","family":"Nurbekyan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,1,19]]},"reference":[{"key":"705_CR1","unstructured":"Ambrosio, L., Gigli, N., Savar\u00e9, G.: Gradient flows in metric spaces and in the space of probability measures, 2nd edn. In: Lectures in Mathematics ETH Z\u00fcrich. Birkh\u00e4user Verlag, Basel (2008)"},{"key":"705_CR2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF02391908","volume":"121","author":"E Asplund","year":"1968","unstructured":"Asplund, E.: Fr\u00e9chet differentiability of convex functions. Acta Math. 121, 31\u201347 (1968)","journal-title":"Acta Math."},{"issue":"2","key":"705_CR3","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1090\/S0002-9947-1987-0902782-7","volume":"303","author":"JM Borwein","year":"1987","unstructured":"Borwein, J.M., Preiss, D.: A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions. Trans. Am. Math. Soc. 303(2), 517\u2013527 (1987)","journal-title":"Trans. Am. Math. Soc."},{"key":"705_CR4","doi-asserted-by":"crossref","unstructured":"Brezis, H.: Functional Analysis. Sobolev Spaces and Partial Ddifferential Equations. Universitext. Springer, New York (2011)","DOI":"10.1007\/978-0-387-70914-7"},{"issue":"1","key":"705_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1983-0690039-8","volume":"277","author":"MG Crandall","year":"1983","unstructured":"Crandall, M.G., Lions, P.-L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277(1), 1\u201342 (1983)","journal-title":"Trans. Am. Math. Soc."},{"key":"705_CR6","doi-asserted-by":"crossref","unstructured":"Crandall, M.G., Lions, P.-L.: Viscosity solutions of Hamilton-Jacobi equations in Banach spaces. In: Trends in the theory and practice of nonlinear analysis (Arlington, Tex., 1984). North-Holland Mathematics Studies, vol. 110, pp. 115\u2013119. North-Holland, Amsterdam (1985)","DOI":"10.1016\/S0304-0208(08)72698-7"},{"issue":"3","key":"705_CR7","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/0022-1236(86)90026-1","volume":"65","author":"MG Crandall","year":"1986","unstructured":"Crandall, M.G., Lions, P.-L.: Hamilton-Jacobi equations in infinite dimensions. II. Existence of viscosity solutions. J. Funct. Anal. 65(3), 368\u2013405 (1986)","journal-title":"J. Funct. Anal."},{"issue":"2","key":"705_CR8","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/0022-1236(86)90005-4","volume":"68","author":"MG Crandall","year":"1986","unstructured":"Crandall, M.G., Lions, P.-L.: Hamilton-Jacobi equations in infinite dimensions. III. J. Funct. Anal. 68(2), 214\u2013247 (1986)","journal-title":"J. Funct. Anal."},{"issue":"2","key":"705_CR9","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0022-1236(90)90084-X","volume":"90","author":"MG Crandall","year":"1990","unstructured":"Crandall, M.G., Lions, P.-L.: Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. IV. Hamiltonians with unbounded linear terms. J. Funct. Anal. 90(2), 237\u2013283 (1990)","journal-title":"J. Funct. Anal."},{"issue":"2","key":"705_CR10","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/0022-1236(91)90010-3","volume":"97","author":"MG Crandall","year":"1991","unstructured":"Crandall, M.G., Lions, P.-L.: Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. V. Unbounded linear terms and $$B$$ B -continuous solutions. J. Funct. Anal. 97(2), 417\u2013465 (1991)","journal-title":"J. Funct. Anal."},{"key":"705_CR11","unstructured":"Crandall, M.G., Lions, P.-L.: Hamilton-Jacobi equations in infinite dimensions. VI. Nonlinear $$A$$ A and Tataru\u2019s method refined. In: Evolution equations, control theory, and biomathematics (Han sur Lesse, 1991). Lecture Notes in Pure and Applied Mathematics, vol. 155, pp. 51\u201389. Dekker, New York (1994)"},{"issue":"1","key":"705_CR12","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1006\/jfan.1994.1119","volume":"125","author":"MG Crandall","year":"1994","unstructured":"Crandall, M.G., Lions, P.-L.: Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. VII. The HJB equation is not always satisfied. J. Funct. Anal. 125(1), 111\u2013148 (1994)","journal-title":"J. Funct. Anal."},{"key":"705_CR13","unstructured":"Deville, R.: Nouveaux principes variationnels. In: S\u00e9minaire d\u2019Initiation \u00e0 l\u2019Analyse, vol. 104. Publ. Math. Univ. Pierre et Marie Curie, Exp. No. 21, 6. Univ. Paris VI, Paris (1990\/91)"},{"issue":"2","key":"705_CR14","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/0022-247X(74)90025-0","volume":"47","author":"I Ekeland","year":"1974","unstructured":"Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47(2), 324\u2013353 (1974)","journal-title":"J. Math. Anal. Appl."},{"issue":"3","key":"705_CR15","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1090\/S0273-0979-1979-14595-6","volume":"1","author":"I Ekeland","year":"1979","unstructured":"Ekeland, I.: Nonconvex minimization problems. Bull. Am. Math. Soc. (N.S.) 1(3), 443\u2013474 (1979)","journal-title":"Bull. Am. Math. Soc. (N.S.)"},{"key":"705_CR16","doi-asserted-by":"crossref","unstructured":"Evans, L.C.: Partial differential equations. In: Graduate Studies in Mathematics, 2nd edn, vol. 19. American Mathematical Society, Providence, RI (2010)","DOI":"10.1090\/gsm\/019"},{"key":"705_CR17","unstructured":"Fathi, A.: Weak KAM Theorem in Lagrangian Dynamics. Cambridge Studies in Advanced Mathematics"},{"issue":"2","key":"705_CR18","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s00205-008-0133-5","volume":"192","author":"J Feng","year":"2009","unstructured":"Feng, J., Katsoulakis, M.: A comparison principle for Hamilton-Jacobi equations related to controlled gradient flows in infinite dimensions. Arch. Ration. Mech. Anal. 192(2), 275\u2013310 (2009)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"705_CR19","volume-title":"Controlled Markov Processes and Viscosity Solutions","author":"WH Fleming","year":"1993","unstructured":"Fleming, W.H., Soner, H.M.: Controlled Markov Processes and Viscosity Solutions. Springer, New York (1993)"},{"key":"705_CR20","unstructured":"Gelfand, I.M., Fomin, S.V.: Calculus of variations. Revised English edition translated and edited by Richard A. Silverman. Prentice-Hall Inc., Englewood Cliffs, N.J. (1963)"},{"key":"705_CR21","unstructured":"Gomes, D., Nurbekyan, L.: Weak kam theory on the $$d$$ d -infinite dimensional torus, in preparation"},{"issue":"1","key":"705_CR22","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.aim.2009.11.005","volume":"224","author":"W Gangbo","year":"2010","unstructured":"Gangbo, W., Tudorascu, A.: Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem. Adv. Math. 224(1), 260\u2013292 (2010)","journal-title":"Adv. Math."},{"key":"705_CR23","unstructured":"Gangbo, W., Tudorascu, A.: A weak KAM theorem; from finite to infinite dimension. In: Optimal Transportation, Geometry and Functional Inequalities. CRM Series, vol. 11, pp. 45\u201372. Ed. Norm., Pisa (2010)"},{"key":"705_CR24","doi-asserted-by":"crossref","unstructured":"Gangbo, W., Tudorascu, A.: Weak kam on the wasserstein torus with multi-dimensional underlying space. Preprint (2012)","DOI":"10.1002\/cpa.21492"},{"issue":"2","key":"705_CR25","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0022-1236(92)90081-S","volume":"105","author":"H Ishii","year":"1992","unstructured":"Ishii, H.: Viscosity solutions for a class of Hamilton-Jacobi equations in Hilbert spaces. J. Funct. Anal. 105(2), 301\u2013341 (1992)","journal-title":"J. Funct. Anal."},{"issue":"2","key":"705_CR26","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0022-247X(92)90256-D","volume":"163","author":"D Tataru","year":"1992","unstructured":"Tataru, D.: Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms. J. Math. Anal. Appl. 163(2), 345\u2013392 (1992)","journal-title":"J. Math. Anal. Appl."}],"container-title":["Calculus of Variations and Partial Differential Equations"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00526-013-0705-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00526-013-0705-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00526-013-0705-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:04:39Z","timestamp":1565107479000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00526-013-0705-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,19]]},"references-count":26,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["705"],"URL":"https:\/\/doi.org\/10.1007\/s00526-013-0705-6","relation":{},"ISSN":["0944-2669","1432-0835"],"issn-type":[{"value":"0944-2669","type":"print"},{"value":"1432-0835","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,19]]}}}