Abstract
We prove global well-posedness of the time-dependent degenerate thermistor problem by establishing a uniform-in-time bounded mean ocsillation (BMO) estimate of inhomogeneous parabolic equations. Applying this estimate to the temperature equation, we derive a BMO bound of the temperature uniform with respect to time, which implies that the electric conductivity is an A2 weight. The Hölder continuity of the electric potential is then proved by applying the De Giorgi-Nash-Moser estimate for degenerate elliptic equations with an A2 coefficient. The uniqueness of the solution is proved based on the established regularity of the weak solution. Our results also imply the existence of a global classical solution when the initial and boundary data are smooth.
Original language | English |
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Article number | e26 |
Pages (from-to) | 1-31 |
Number of pages | 31 |
Journal | Forum of Mathematics, Sigma |
Volume | 3 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
ASJC Scopus subject areas
- Analysis
- Theoretical Computer Science
- Algebra and Number Theory
- Statistics and Probability
- Mathematical Physics
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Mathematics