Sobolev spaces with mixed weights and the Poisson equation on angular domains

• DOI: 10.48550/arxiv.2409.18615
• Publication Date: 2024-09-27
• Authors: Petru A. Cioica-L...; Cornelia Schneider; Markus Weimar
• Keywords: Poisson's equation

We introduce and analyse a class of weighted Sobolev spaces with mixed weights on angular domains. The are based both the distance to boundary one vertex domain. Moreover, we show how regularity Poisson equation can be analysed in framework these by means Mellin transform, provided integrability parameter equals two. Our main motivation comes from study stochastic partial differential equations associated degenerate deterministic parabolic equations.