{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T06:05:40Z","timestamp":1773209140099,"version":"3.50.1"},"reference-count":28,"publisher":"American Mathematical Society (AMS)","issue":"10","license":[{"start":{"date-parts":[[2025,8,9]],"date-time":"2025-08-09T00:00:00Z","timestamp":1754697600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100007474","name":"Centro de Matem\u00c3\u00a1tica, Universidade de Coimbra","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007474","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>\n                    We prove that minimizers of the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L Superscript d\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>d<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^{d}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -norm of the Hessian in the unit ball of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper R Superscript d\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {R}^d<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are locally of class\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C Superscript 1 comma alpha\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">C^{1,\\alpha }<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the H\u00f6lder regularity theory available for elliptic equations in double-divergence form.\n                  <\/p>","DOI":"10.1090\/proc\/16894","type":"journal-article","created":{"date-parts":[[2024,5,1]],"date-time":"2024-05-01T10:54:00Z","timestamp":1714560840000},"page":"4393-4403","source":"Crossref","is-referenced-by-count":0,"special_numbering":"784","title":["Improved regularity for a Hessian-dependent functional"],"prefix":"10.1090","volume":"152","author":[{"given":"Vincenzo","family":"Bianca","sequence":"first","affiliation":[]},{"given":"Edgard","family":"Pimentel","sequence":"additional","affiliation":[]},{"given":"Jos\u00e9","family":"Urbano","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,8,9]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics (Amsterdam)","isbn-type":"print","volume-title":"Sobolev spaces","volume":"140","author":"Adams, Robert A.","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/0120441438","edition":"2"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s11854-021-0193-0","article-title":"Stationary fully nonlinear mean-field games","volume":"145","author":"Andrade, P\u00eadra D. 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