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Analysis

International mathematical journal of analysis and its applications


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Band 37, Heft 4

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Existence of variational solutions for time dependent integrands via minimizing movements

Leah Schätzler
  • Korrespondenzautor
  • Department Mathematik, Friedrich-Alexander-Universität Erlangen–Nürnberg, Cauerstraße 11, 91058 Erlangen, Germany
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Online erschienen: 25.10.2017 | DOI: https://doi.org/10.1515/anly-2017-0047

Abstract

We prove the existence of variational solutions to equations of the form

tu-div(Dξf(x,t,Du))=0,

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 (p,q)-growth.

Keywords: minimizing movements

MSC 2010: 35K20; 49J40

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Artikelinformationen

Erhalten: 21.09.2017

Angenommen: 21.09.2017

Online erschienen: 25.10.2017

Erschienen im Druck: 01.11.2017


Quellenangabe: Analysis, Band 37, Heft 4, Seiten 199–222, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2017-0047.

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