Besov regularity of parabolic and hyperbolic PDEs

Dahlke S, Schneider C (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Analysis and Applications World Scientific Publishing

Book Volume: 17

Pages Range: 235-291

Journal Issue: 2

DOI: 10.1142/S0219530518500306

Abstract

This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations on nonsmooth domains. In particular, we study the smoothness in the specific scale B-tau,tau(r), 1/tau = r/d + 1/p of Besov spaces. The regularity in these spaces determines the approximation order that can be achieved by adaptive and other nonlinear approximation schemes. We show that for all cases under consideration the Besov regularity is high enough to justify the use of adaptive algorithms.

Authors with CRIS profile

Cornelia Schneider Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)

Related research project(s)

Besov Regularität von parabolischen partiellen Differentialgleichungen auf Lipschitz Gebieten April 1, 2017 - March 31, 2019

Involved external institutions

Philipps-Universität Marburg DE Germany (DE)

How to cite

APA:

Dahlke, S., & Schneider, C. (2019). Besov regularity of parabolic and hyperbolic PDEs. Analysis and Applications, 17(2), 235-291. https://doi.org/10.1142/S0219530518500306

MLA:

Dahlke, Stephan, and Cornelia Schneider. "Besov regularity of parabolic and hyperbolic PDEs." Analysis and Applications 17.2 (2019): 235-291.

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