Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 415-443
Universität Erlangen-Nürnberg, Department Mathematik
Cauerstrasse 11, 91058 Erlangen, Germany; scheven 'at' mi.uni-erlangen.de
Abstract. For parabolic obstacle problems with quadratic growth, we give pointwise estimates both for the solutions and their gradients in terms of potentials of the given data. As applications, we derive Lorentz space estimates if the data satisfies the corresponding Lorentz space regularity. Moreover, we discuss a borderline case in the regularity theory, the question of boundedness and continuity of the gradients as well as of the solutions itself.
2010 Mathematics Subject Classification: Primary 35K86, 35B65, 31B35.
Key words: Parabolic obstacle problems, regularity of solutions, non-linear potential theory.
Reference to this article: C. Scheven: Potential estimates in parabolic obstacle problems. Ann. Acad. Sci. Fenn. Math. 37 (2012), 415-443.
doi:10.5186/aasfm.2012.3730
Copyright © 2012 by Academia Scientiarum Fennica