Some remarks on a class of weight functions

summary:In this paper we obtain some results about a class of functions $\rho\,:\, \Omega\rightarrow R_+$, where $\Omega$ is an open set of $R^n$, which are related to the distance function from a fixed subset $S_\rho\subset\partial\Omega$. We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function $\rho$

dirichlet problem for divergence form elliptic equations with discontinuous coefficients

We study the Dirichlet problem for linear elliptic second order partial differential equations with discontinuous coefficients in divergence form in unbounded domains. We establish an existence and uniqueness result and we prove an a priori bound in L p Open image in new window, p > 2 Open image in new window

The Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains of the plane

This paper deals with the Dirichlet problem for second order linear elliptic equations in unbounded domains of the plane in weighted Sobolev spaces. We prove an a priori bound and an existence and uniqueness result

A weighted W2,p-a priori bound for a class of elliptic operators

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Solvability of the Dirichlet Problem for Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We state a regularity result and we can deduce an existence and uniqueness theorem

A strong maximum principle for linear elliptic operators

This paper is concerned with a maximum principle for subsolutions, in the class W^{2,p}_loc, of second order linear elliptic equations in nondivergence form in arbitrary open (bounded or not) subsets of R^n, n >=2, when p > n/2

A priori bounds for elliptic operators in weighted Sobolev spaces

This paper is concerning with the study of a class of weight functions and their properties. As an application, we prove some a priori bounds for a class of uniformly elliptic second order linear differential operators in weighted Sobolev spaces

Weighted a priori bounds for elliptic operators of Cordes type

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Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

We study in this paper a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem

uniqueness results for the dirichlet problem for higher order elliptic equations in polyhedral angles

We consider the Dirichlet boundary value problem for higher order elliptic equations in divergence form with discontinuous coefficients in polyhedral angles. Some uniqueness results are proved