Extension of an integral inequality of C. Miranda and applications to the elliptic equations with discontinuous coefficients

Albino Canfora

Displaying similar documents to “Extension of an integral inequality of C. Miranda and applications to the elliptic equations with discontinuous coefficients”

Some Developments on Dirichlet Problems with Discontinuous Coefficients

Lucio Boccardo (2009)

Bollettino dell'Unione Matematica Italiana

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This paper, dedicated to the memory of Guido Stampacchia in the thirtieth anniversary of his death, starts from his lectures on Dirichlet problems of forty years ago. As Sergei Prokofiev named his first symphony the "Classical", since it was written in the style that Joseph Haydn would have used if he had been alive at the time, this paper strongly follows the one by Guido Stampacchia about elliptic equations with discontinuous coefficients ([8]).

The Probabilistic Solution of the Dirichlet Problem for Degenerate Elliptic Equations

Chuandi Liu, Hiroaki Morimoto (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study the Dirichlet problem for degenerate elliptic equations, and show that the probabilistic solution is a unique viscosity solution.

Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

Mikhail Borsuk (1998)

Annales Polonici Mathematici

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We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives.

Semilinear elliptic problems in unbounded domains

Aleksandra Orpel (2006)

Applicationes Mathematicae

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We investigate the existence of positive solutions and their continuous dependence on functional parameters for a semilinear Dirichlet problem. We discuss the case when the domain is unbounded and the nonlinearity is smooth and convex on a certain interval only.

Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators

Nikolai Nadirashvili (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On existence of a unique generalized solution to systems of elliptic PDEs at resonance

Tiantian Qiao, Weiguo Li, Kai Liu, Boying Wu (2014)

Annales Polonici Mathematici

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The Dirichlet boundary value problem for systems of elliptic partial differential equations at resonance is studied. The existence of a unique generalized solution is proved using a new min-max principle and a global inversion theorem.