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Journal of Evolution Equations

, Volume 17, Issue 4, pp 1273–1310 | Cite as

The obstacle problem for parabolic minimizers

  • Verena Bögelein
  • Frank Duzaar
  • Christoph SchevenEmail author
Article

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.

Keywords

Evolutionary p-Laplacian Obstacle problem Minimizing movements 

Mathematics Subject Classification

35K86 35K20 49J40 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Verena Bögelein
    • 1
  • Frank Duzaar
    • 2
  • Christoph Scheven
    • 3
    Email author
  1. 1.Fachbereich MathematikUniversität SalzburgSalzburgAustria
  2. 2.Department MathematikUniversität Erlangen-NürnbergErlangenGermany
  3. 3.Fakultät für MathematikUniversität Duisburg-EssenEssenGermany

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