Existence of variational solutions for time dependent integrands via minimizing movements
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Leah Schätzler
Abstract
We prove the existence of variational solutions to equations of the form
where the function f merely satisfies a p-growth condition and is convex with respect to the gradient variable.
In particular, we do not require any regularity assumption with respect to time.
We obtain an existence result for integrands that are Lipschitz continuous in time via the method of minimizing movements.
For the general existence result, we show stability of solutions with respect to approximation of the integrands.
In this context, we prove a result related to Γ-convergence that is also valid for functionals with
Acknowledgements
I thank my adviser, Professor Frank Duzaar, for giving me this interesting topic and for his helpful remarks. I also thank Professor Jan Kristensen (Oxford), who has suggested the use of the bi-polar construction in Section 3.
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- s-convex functions on discrete time domains
- Ulam–Hyers stability of hexadecic functional equations in multi-Banach spaces
- Existence of variational solutions for time dependent integrands via minimizing movements
- Enclosure theorems and barrier principles for energy stationary currents and the associated Brakke-flow
-
Remarks on
Articles in the same Issue
- Frontmatter
- s-convex functions on discrete time domains
- Ulam–Hyers stability of hexadecic functional equations in multi-Banach spaces
- Existence of variational solutions for time dependent integrands via minimizing movements
- Enclosure theorems and barrier principles for energy stationary currents and the associated Brakke-flow
-
Remarks on
