Second order elliptic operators in $L^2$ with first order degeneration at the boundaryand outward pointing drift
Simona Fornaro, Giorgio Metafune, Diego Pallara, Roland Schnaubelt · Communications on Pure & Applied Analysis · 2015
We study second order elliptic operators whose diffusion coefficientsdegenerate at the boundary in first order and whose drift term stronglypoints outward. It is shown that these operators generate analytic semigroups in $L^2$where they are equipped with their natural domain without boundary conditions. Hence,the corresponding parabolic problem can be solved with optimal regularity.In a previous work we had treated the case of inward pointing drift terms.