Abstract
Second order elliptic operators and their parabolic counterparts are studied in the case of complete boundary degeneration of the leading order coefficients in the presence of a strong outward pointing drift. It is shown that the problem generates a positive analytic \(C_0\)-semigroup with maximal \(L_p\)-regularity in \(L_q\)-spaces. This result is based on hard analysis estimates for integral operators in combination with modern functional analytic tools like \({\mathcal R}\)-boundedness and the operator-valued functional calculus.
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Prüss, J. On second-order elliptic operators with complete first-order boundary degeneration and strong outward drift. Arch. Math. 108, 301–311 (2017). https://doi.org/10.1007/s00013-016-0992-1
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DOI: https://doi.org/10.1007/s00013-016-0992-1