Abstract
As an application of the theory of linear parabolic differential equations on noncompact Riemannian manifolds, developed in earlier papers, we prove a maximal regularity theorem for nonuniformly parabolic boundary value problems in Euclidean spaces. The new feature of our result is the fact that—besides of obtaining an optimal solution theory—we consider the ‘natural’ case where the degeneration occurs only in the normal direction.
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Notes
As usual, we use the same symbol for a Riemannian metric and its restrictions to submanifolds.
If V is a vector bundle over M, then \(C^k(V)\) denotes the vector space of \(C^k\) sections of V.
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Amann, H. Linear parabolic equations with strong boundary degeneration. J Elliptic Parabol Equ 6, 123–144 (2020). https://doi.org/10.1007/s41808-020-00061-1
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DOI: https://doi.org/10.1007/s41808-020-00061-1