DIRICHLET PROBLEM FOR ELLIPTIC EQUATIONS IN WEIGHTED SOBOLEV SPACES

Weighted Sobolev Spaces and Degenerate Elliptic Equations

In the case ω = 1, this space is denoted W (Ω). Sobolev spaces without weights occur as spaces of solutions for elliptic and parabolic partial differential equations. In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is “disturbed” in the sense that some degeneration or singularity appears. This “bad” behaviour can be caused by the coefficient...

A Priori Estimates for Elliptic Equations in Weighted Sobolev Spaces

In this paper we prove some a priori bounds for the solutions of the Dirichlet problem for elliptic equations with singular coefficients in weighted Sobolev spaces. Mathematics subject classification (2010): 35J25, 35B45, 35R05.

Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

NEUMANN PROBLEM FOR NON-DIVERGENCE ELLIPTIC AND PARABOLIC EQUATIONS WITH BMOx COEFFICIENTS IN WEIGHTED SOBOLEV SPACES

We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only measurable in the time variable and have small mean oscillations in the spatial variables. Our results can be applied to Neumann boundary value problems for stochast...

Sobolev Spaces and Elliptic Equations

Lipschitz domains. Our presentations here will almost exclusively be for bounded Lipschitz domains. Roughly speaking, a domain (a connected open set) Ω ⊂ R is called a Lipschitz domain if its boundary ∂Ω can be locally represented by Lipschitz continuous function; namely for any x ∈ ∂Ω, there exists a neighborhood of x, G ⊂ R, such that G ∩ ∂Ω is the graph of a Lipschitz continuous function und...