Differential Equations

, Volume 55, Issue 8, pp 1056–1068 | Cite as

Hölder Continuity of Solutions of an Elliptic p(x)-Laplace Equation Uniformly Degenerate on a Part of the Domain

  • Yu. A. AlkhutovEmail author
  • S. T. HuseynovEmail author
Partial Differential Equations


In a domain D ⊂ ℝn divided by a hyperplane Σ into two parts D(1) and D(2), we consider a p(x)-Laplace type equation with a small parameter and with exponent p(x) that has a logarithmic modulus of continuity in each part of the domain and undergoes a jump on Σ when passing from D(2) to D(1). Under the assumption that the equation uniformly degenerates with respect to the small parameter in D(1), we establish the Hölder continuity of solutions with Hölder exponent independent of the parameter.


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The authors are grateful to the referee for comments and suggestions, which have improved the exposition of the results of the present paper.


The research by Yu.A. Alkhutov was supported by the RF Ministry of Education and Science, project no. 1.3270.2017/4.6.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Stoletovs’ Vladimir State UniversityVladimirRussia
  2. 2.Baku State UniversityBakuAzerbaijan

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