The obstacle problem for parabolic minimizers

Bögelein V, Duzaar F, Scheven C (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Journal of Evolution Equations Springer Verlag (Germany)

Book Volume: 17

Pages Range: 1273--1310

Journal Issue: 4

DOI: 10.1007/s00028-017-0384-4

Abstract

We prove an existence result for parabolic minimizers of convex variational functionals with p-growth and irregular obstacles. In particular, the obstacle might be unbounded, discontinuous and satisfy no regularity assumption with respect to the time variable. Moreover, we treat the case of obstacles which do not coincide along the parabolic boundary with the prescribed time-dependent Dirichlet boundary values. The existence result for sufficiently regular obstacles coinciding on the lateral boundary with the given Dirichlet boundary values is obtained via the method of minimizing movements. More general boundary values and obstacles are treated by approximation with regular boundary values and obstacles in the sense of a stability result of solutions with respect to boundary values and the obstacles.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

Universität Salzburg (Paris Lodron Universität Salzburg) AT Austria (AT) Universität Duisburg-Essen (UDE) DE Germany (DE)

How to cite

APA:

Bögelein, V., Duzaar, F., & Scheven, C. (2017). The obstacle problem for parabolic minimizers. Journal of Evolution Equations, 17(4), 1273--1310. https://dx.doi.org/10.1007/s00028-017-0384-4

MLA:

Bögelein, Verena, Frank Duzaar, and Christoph Scheven. "The obstacle problem for parabolic minimizers." Journal of Evolution Equations 17.4 (2017): 1273--1310.

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