Elliptic and Parabolic Equations - Abstract

Nittka, Robin

Well-posedness of parabolic equations with Robin boundary conditions on Lipschitz domains

The first part of the talk concerns a flexible approach how boundary regularity of solutions of linear elliptic problems with Robin boundary conditions on Lipschitz domains can be deduced from interior regularity results via an extension-by-reflection argument. In the second part it is shown how this can be applied to prove that elliptic operators with Robin or Wentzell--Robin boundary conditions generate strongly continuous semigroups on the space of continuous functions.