Regularity of solutions of linear second order elliptic and parabolic boundary value problems on Lipschitz domains

By Robin Nittka. 2009

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For a linear, strictly elliptic second order differential operator in divergence form with bounded, measurable coefficients on a Lipschitz domain Ω we show that solutions of the corresponding elliptic problem with Robin and thus in particular with Neumann boundary conditions are Holder continuous up to the boundary for sufficiently Lp-regular right-hand sides. From this we deduce that the parabolic problem with Robin or Wentzell–Robin boundary conditions is well-posed on C(Ω¯).

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e95d5a32a5d149614b00d37393ef3e54cd555a19