Extension of an integral inequality of C. Miranda and applications to the elliptic equations with discontinuous coefficients
Albino Canfora (1989)
Czechoslovak Mathematical Journal
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Displaying similar documents to “The Probabilistic Solution of the Dirichlet Problem for Degenerate Elliptic Equations”
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]).
BSDEs with random terminal time and semilinear elliptic PDEs in divergence form
Andrzej Rozkosz (2005)
Studia Mathematica
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We study connections between Sobolev space solutions of the Dirichlet problem for semilinear second order elliptic equations in divergence form and solutions of backward stochastic differential equations with random terminal time.
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.
Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms
Tomasz Klimsiak, Andrzej Rozkosz (2016)
Colloquium Mathematicae
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We are mainly concerned with equations of the form -Lu = f(x,u) + μ, where L is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, f satisfies the monotonicity condition and mild integrability conditions, and μ is a bounded smooth measure. We prove general results on existence, uniqueness and regularity of probabilistic solutions, which are expressed in terms of solutions to backward stochastic differential equations. Applications include equations with...
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.
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.
On fully nonlinear elliptic equations of second order
L. Nirenberg (1988-1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
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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 the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions.
Z.Q. Chen, R.J. Williams, Z. Zhao (1994)
Mathematische Annalen
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