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Hölder continuous solutions of an obstacle thermistor problem. (English) Zbl 1099.35183
The authors obtain a regularity result for the solution of an obstacle thermistor problem. The nonlinear problem studied has nonlocal boundary condition and the existence of a Hölder continuous \(C^{\alpha,\alpha/2}\) solution represents the center focus of the article. The proof is based on a penalized method introduced by the authors in a previous article and also a technique that involves the Leray-Schauder degree theory along with results for Campanato spaces. Using a decomposition method for transforming the equation satisfied by the electric potential into two elliptic problems, it is proved, first, the existence of \(C^{\alpha,\alpha/2}\) solutions for the penalized equations and then, a solution of the original obstacle system is obtained by passing to the limit of some subsequence of the penalized solutions.

35R45 Partial differential inequalities and systems of partial differential inequalities
49J40 Variational inequalities
74F15 Electromagnetic effects in solid mechanics
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