1 Giugno, 2016 16:15 in punto

Sezione di Analisi

A Meyers-Serrin Theorem for Degenerate Sobolev Spaces with an application to degenerate $p$-Laplacians

Scott Rodney, Cape Breton University, Canada

Aula seminari 3° piano

It is well understood that degenerate elliptic PDEs in divergence form play an important role in many areas of mathematics. For a non-negative definite measurable matrix valued function $A(x)$ and $1?p<\infty$, the degenerate matrix-weighted Sobolev spaces $H^{1,p}_A(\Omega)$ (defined as a closure of $C^\infty(\Omega)$) and $W^{1,p}_A(\Omega)$ (defined as a collection of functions with locally integrable distributional derivatives) play a central role in regularity theory and applications. In this talk, I present joint work with D. Cruz-Uribe and K. Moen that gives a sharp condition on the matrix function A for the equality $H^{1,p}_A(\Omega) = W^{1,p}_A(\Omega)$.