Displaying similar documents to “De Giorgi’s Theorem, for a Class of Strongly Degenerate Elliptic Equations”

De Giorgi’s Theorem, for a Class of Strongly Degenerate Elliptic Equations

Bruno Franchi, Ermanno Lanconelli (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In questa Nota enunciamo, per una classe di equazioni ellittiche del secondo ordine «fortemente degeneri» a coefficienti misurabili, un teorema di hölderianità delle soluzioni deboli che estende il ben noto risultato di De Giorgi e Nash. Tale risuJtato discende dalle proprietà geometriche di opportune famiglie di sfere associate agli operatori.

Continuity of solutions of linear, degenerate elliptic equations

Jani Onninen, Xiao Zhong (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.

Estimates on elliptic equations that hold only where the gradient is large

Cyril Imbert, Luis Silvestre (2016)

Journal of the European Mathematical Society

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We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.

Caccioppoli sets

Mario Miranda (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The story of the theory of Caccioppoli sets is presented, together with some information about Renato Caccioppoli’s life. The fundamental contributions of Ennio De Giorgi to the theory of Caccioppoli sets are sketched. A list of applications of Cacciopoli sets to the calculus of variations is finally included.