Regularity of Weak Solutions to a Model Problem with Conjugation Conditions for Quasilinear Parabolic Systems of Equations
- Authors: Arkhipova A.A.1
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Affiliations:
- St. Petersburg State University
- Issue: Vol 219, No 6 (2016)
- Pages: 850-873
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238722
- DOI: https://doi.org/10.1007/s10958-016-3151-0
- ID: 238722
Cite item
Abstract
We consider a parabolic quasilinear second order system of equations in divergence form in a model parabolic cylinder. We prove the Hölder continuity of a weak solution on a set of full measure in the cylinder. It is shown that the linear system has no singular set. We use a modified method of A-caloric approximation which takes into account the conjugation conditions on the interface between media.
About the authors
A. A. Arkhipova
St. Petersburg State University
Author for correspondence.
Email: arinaark@gmail.com
Russian Federation, 28, Universitetskii pr., Petrodvorets, St. Petersburg, 198504