Geodesic
UNIFORM BMO ESTIMATE OF PARABOLIC EQUATIONS AND GLOBAL WELL-POSEDNESS OF THE THERMISTOR PROBLEM
Forum of Mathematics, Sigma, Tome 3 (2015)

Voir la notice de l'article provenant de la source Cambridge University Press

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 $A_{2}$ 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 $A_{2}$ 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. 
@article{10_1017_fms_2015_29,
     author = {BUYANG LI and CHAOXIA YANG},
     title = {UNIFORM {BMO} {ESTIMATE} {OF} {PARABOLIC} {EQUATIONS} {AND} {GLOBAL} {WELL-POSEDNESS} {OF} {THE} {THERMISTOR} {PROBLEM}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {3},
     year = {2015},
     doi = {10.1017/fms.2015.29},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2015.29/}
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BUYANG LI; CHAOXIA YANG. UNIFORM BMO ESTIMATE OF PARABOLIC EQUATIONS AND GLOBAL WELL-POSEDNESS OF THE THERMISTOR PROBLEM. Forum of Mathematics, Sigma, Tome 3 (2015). doi: 10.1017/fms.2015.29

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