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. In the present work, we establish pointwise estimates by potentials for solutions to parabolic obstacle problems. Obstacle problems play a prominent role in various applications, for example in mechanics or control theory, cf. (4, 22), but also in other fields of mathematics such as potential theory, where solutions to obstacle problems prove useful as approximations of super-solutions (16, 18, 23). Here, we treat obstacle problems that are related to equations of the type
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