Advances in Differential Equations

Hölder continuity of solutions to parabolic equations uniformly degenerating on a part of the domain

Yury A. Alkhutov and Vitali Liskevich

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Abstract

We study a second-order parabolic equation in divergence form in a spatial domain separated in two parts by a hyperplane. The equation is uniformly parabolic in one of the parts and degenerates with respect to a small parameter $\varepsilon$ on the other part. We show that weak solutions to this equation are Hölder continuous with the Hölder exponent independent of ${\varepsilon}$.

Article information

Source
Adv. Differential Equations Volume 17, Number 7/8 (2012), 747-766.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355702975

Mathematical Reviews number (MathSciNet)
MR2963803

Subjects
Primary: 35B65: Smoothness and regularity of solutions 35K10: Second-order parabolic equations

Citation

Alkhutov, Yury A.; Liskevich, Vitali. Hölder continuity of solutions to parabolic equations uniformly degenerating on a part of the domain. Adv. Differential Equations 17 (2012), no. 7/8, 747--766. https://projecteuclid.org/euclid.ade/1355702975.


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