Explicit higher regularity on a Cauchy problem with mixed Neumann-power type boundary conditions

Abstract

We investigate the regularity in $L^p$ ($p>2$) of the gradient of any weak solution of a Cauchy problem with mixed Neumann-power type boundary conditions. Under suitable assumptions we prove the existence of weak solutions that satisfy explicit estimates. Some considerations on the steady-state regularity are discussed.

arXiv comment26 pages