# FALL 2020 Nonlinear Analysis Seminar Series

### Date

Thursday, November 5, 2020 - 16:00 to 17:00

on Zoom

### Abstract:

We discuss solvability of Dirichlet problems of the type $$- \Delta_{p} u = \mu$$ in $$\Omega$$, $$u = 0$$ on $$\partial \Omega$$, where $$\Omega$$ is a bounded domain, $$\Delta_{p}$$ is the p-Laplacian, and $$\mu$$ is a nonnegative locally finite Radon measure on $$\Omega$$. We do not assume the finiteness of $$\mu(\Omega)$$ here. We revisit this problem with a potential theoretic viewpoint and give sufficient conditions for the existence of solutions. Our main tools are $$L^{p}(dx)-L^{q}(d \mu)$$ trace inequalities and capacitary conditions. Also, we derive the trace inequalities using solutions conversely.