A WEIGHTED L-p-THEORY FOR SECOND-ORDER PARABOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL SYSTEMS ON A HALF SPACE

초록

this article we consider parabolic systems and L-p regularity of the solutions. With zero boundary condition the solutions experience bad regularity near the boundary. This article addresses a possible way of describing the regularity nature. Our space domain is a half space and we adapt an appropriate weight into our function spaces. In this weighted Sobolev space setting we develop a Fefferman-Stein theorem, a Hardy-Littlewood theorem and sharp function estimations. Using these, we prove uniqueness and existence results for second-order elliptic and parabolic partial differential systems in weighed Sobolev spaces.

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