Degenerate operators of Tricomi type in Lp - spaces and in spaces of continuous functions
Date: 23. 12. 2010
We study elliptic operators $L$ with Dirichlet boundary conditions on a bounded domain $\Omega$ whose diffusion coefficients degenerate linearly at $\partial\Omega$ in tangential directions. We compute the domain of $L$ and establish existence, uniqueness and (maximal) regularity of the elliptic and parabolic problems for $L$ in $L^p$--spaces and in spaces of continuous functions. Moreover, the analytic semigroups generated by $L$ are consistent, positive, compact and exponentially stable.
Primary MSC: 35J70 Degenerate elliptic equations , 35K65 Degenerate parabolic equations