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arXiv:1903.11224 [math.AP]AbstractReferencesReviewsResources

Existence and Regularity of Weak Solutions to a Thermoelectric Model

Xing-Bin Pan, Zhibing Zhang

Published 2019-03-27Version 1

This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of the equations, and with the help of the De Giorgi-Nash estimate for elliptic equations, we obtain existence of weak solutions on Lipschitz domains for general boundary data. Using Campanato's method, we establish regularity results of the weak solutions.

Comments: provisionally accepted by Nonlinearity
Categories: math.AP
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