Regularity of solutions to a model oblique derivative problem for quasilinear parabolic systems with nondiagonal principal matrices

A. A. Arkhipova, G. V. Grishina

Research output

2 Citations (Scopus)

Abstract

We consider quasilinear parabolic systems of equations with nondiagonal principal matrices. The oblique derivative of a solution is defined on the plane part of the lateral surface of a parabolic cylinder. We do not assume smoothness of the principal matrix and the boundary functions in the time variable and prove partial Hölder continuity of a weak solution near the plane part of the lateral surface of the cylinder. Hölder continuity of weak solutions to the correspondent linear problem is stated. A modification of the A(t)-caloric approximation method is applied to study the regularity of weak solutions.

Translated title of the contributionРегулярность решений модельной задачи с косой прлоизводной для квазилинейных параболических систем с недиагональными главными матрицами
Original languageEnglish
Pages (from-to)1-18
JournalVestnik St.Petersburg University
Volume52
Issue number1
DOIs
Publication statusPublished - 2019

Scopus subject areas

  • Mathematics(all)

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