The obstacle problem for parabolic minimizers

Bögelein V, Duzaar F, Scheven C (2017)

Publication Type: Journal article

Publication year: 2017


Book Volume: 17

Pages Range: 1273--1310

Journal Issue: 4

DOI: 10.1007/s00028-017-0384-4


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.

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Bögelein, V., Duzaar, F., & Scheven, C. (2017). The obstacle problem for parabolic minimizers. Journal of Evolution Equations, 17(4), 1273--1310.


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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