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.
Constantin BacutaVictor NistorLudmil T. ZikatanovLUDMIL T. ZIKATANOV
We prove a well-posedness result for second order boundary value problems in weighted Sobolev spaces on curvilinear polyhedral domains in Rn with Dirichlet boundary conditions. Our typical weight is the distance to the set of singular boundary points.
In this work we characterize boundedness and compactness of weighted composition operators acting between Dirichlet type spaces by using Carleson measures. We also find essential norm estimates for these operators.
