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Second order elliptic operators in $L^2$ with first order degeneration at the boundary and outward pointing drift

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  • We study second order elliptic operators whose diffusion coefficients degenerate at the boundary in first order and whose drift term strongly points 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.
    Mathematics Subject Classification: Primary: 35K65, 35J70.


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