Displaying similar documents to “Elliptic regularity and essential self-adjointness of Dirichlet operators on ℝ n ”

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...

The Dirichlet problem for elliptic equations with drift terms.

Carlos E. Kenig, Jill Pipher (2001)

Publicacions Matemàtiques

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We establish absolute continuity of the elliptic measure associated to certain second order elliptic equations in either divergence or nondivergence form, with drift terms, under minimal smoothness assumptions on the coefficients.