Singular parabolic equations of second order on manifolds with singularities

Abstract

The main aim of this article is to establish an $L_p$-theory for elliptic operators on manifolds with singularities. The particular class of differential operators discussed herein may exhibit degenerate or singular behavior near the singular ends of the manifolds. Such a theory is of importance for the study of elliptic and parabolic equations on non-compact, or even incomplete manifolds, with or without boundary.

References in corpus (2)

• Anisotropic Function Spaces on Singular Manifolds
• The Yamabe flow on incomplete manifolds

Cited by in corpus (5)

• The Yamabe flow on incomplete manifolds
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• Existence and maximal $L^p$-regularity of solutions for the porous medium equation on manifolds with conical singularities
• Function Spaces on Uniformly Regular and Singular Riemannian Manifolds
• Maximal $L_q$-regularity of nonlocal parabolic equations in higher order Bessel potential spaces