21 Febbraio, 2018 15:15

Sezione di Analisi

Poincaré-Sobolev Inequalities and the p-Laplacian

Scott Rodney, Cape Breton University

Aula seminari 3° piano

It is well known that Poincar\'e-Sobolev inequalities play an important role in applications and in regularity theory for weak solutions of PDEs. In this talk I will discuss two new results connecting matrix weighted Poincar\'e-Sobolev estimates to the existence of regular weak solutions of Dirichlet and Neumann problems for a degenerate $p$-Laplacian:
\begin{eqnarray}
\Delta_{Q,p} \varphi(x) = \textrm{Div}\left(\big|Q(x)~\nabla \varphi(x)\big|^{p-2}~Q(x)~\nabla\varphi(x)\right).\nonumber
\end{eqnarray}
Degeneracy of $\Delta_{Q,p}$ is given by a measurable non-negative definite matrix-valued function $Q(x)$.