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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Albino Canfora (1989)
Czechoslovak Mathematical Journal
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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]).
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.
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.
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...
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.
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.
L. Nirenberg (1988-1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Nikolai Nadirashvili (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Z.Q. Chen, R.J. Williams, Z. Zhao (1994)
Mathematische Annalen
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N. Kutev (1991)
Archivum Mathematicum
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