Existence and regularity of weak solutions for a thermoelectric model

Abstract

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 analysing carefully the nonlinear structure of the equations, and with the help of the De Giorgi-Nash estimate for elliptic equations, we obtain weak solutions in Lipschitz domains for general boundary data. Using Campanato's method, we obtain regularity results for the weak solutions.

Singular limit of Lamé equations

“…As we all know, it is difficult and interesting to study degenerate equations. One can see 6 for the second-order degenerate equations and [7][8][9][10][11] for the Maxwell equations. An observation is that the Lamé equations and the Maxwell-type system admit different kinds of boundary conditions.…”

“…As we all know, it is difficult and interesting to study degenerate equations. One can see 6 for the second‐order degenerate equations and 7–11 for the Maxwell equations.…”