Regularity of weak solutions to a model problem with conjugation conditions for quasilinear parabolic systems

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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.
Translated title of the contributionРегулярность обобщенных решений модельной задачи с условиями сопряжения для квазилинейных параболических систем уравнений
Original languageEnglish
Pages (from-to)850-873
Number of pages23
JournalJournal of Mathematical Sciences
Volume219
Issue number6
Early online date8 Nov 2016
Publication statusPublished - 2016

Scopus subject areas

  • Mathematics(all)

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