Displaying similar documents to “BSDEs with random terminal time and semilinear elliptic PDEs in divergence form”

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.

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...

Generalized RBSDEs with Random Terminal Time and Applications to PDEs

Katarzyna Jańczak-Borkowska (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Generalized reflected backward stochastic differential equations have been considered so far only in the case of a deterministic interval. In this paper the existence and uniqueness of solution for generalized reflected backward stochastic differential equations in a convex domain with random terminal time is studied. Applications to the obstacle problem with Neumann boundary conditions for partial differential equations of elliptic type are given.

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]).

Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential

Guillaume Bal, Wenjia Jing (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper analyzes the random fluctuations obtained by a heterogeneous multi-scale first-order finite element method applied to solve elliptic equations with a random potential. Several multi-scale numerical algorithms have been shown to correctly capture the homogenized limit of solutions of elliptic equations with coefficients modeled as stationary and ergodic random fields. Because theoretical results are available in the continuum setting for such equations, we consider here the...

On the convergence of the stochastic Galerkin method for random elliptic partial differential equations

Antje Mugler, Hans-Jörg Starkloff (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity...

Symmetry of solutions of semilinear elliptic problems

Jean Van Schaftingen, Michel Willem (2008)

Journal of the European Mathematical Society

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We study symmetry properties of least energy positive or nodal solutions of semilinear elliptic problems with Dirichlet or Neumann boundary conditions. The proof is based on symmetrizations in the spirit of Bartsch, Weth and Willem (J. Anal. Math., 2005) together with a strong maximum principle for quasi-continuous functions of Ancona and an intermediate value property for such functions.