Hölder Continuity of Solutions of an Elliptic p(x)-Laplace Equation Uniformly Degenerate on a Part of the Domain
- 1 Downloads
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.
Unable to display preview. Download preview PDF.
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.
- 3.Růžička, M., Electrorheological Fluids: Modeling and Mathematical Theory, in Lect. Notes Math., Berlin–New York: Springer, 2000, Vol. 1748.Google Scholar
- 9.Alkhutov, Yu.A. and Surnachev, M.D., A Harnack inequality for a transmission problem with p(x)-Laplacian, Appl. Anal., 2018, doi: 10.1080/00036811.2017.1423473.Google Scholar