Weighted energy-dissipation functionals for doubly nonlinear evolution

Goro Akagi, Ulisse Stefanelli

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

This paper is concerned with the Weighted Energy-Dissipation (WED) functional approach to doubly nonlinear evolutionary problems. This approach consists in minimizing (WED) functionals defined over entire trajectories. We present the features of the WED variational formalism and analyze the related Euler-Lagrange problems. Moreover, we check that minimizers of the WED functionals converge to the corresponding limiting doubly nonlinear evolution. Finally, we present a discussion on the functional convergence of sequences of WED functionals and present some application of the abstract theory to nonlinear PDEs.

Original languageEnglish
Pages (from-to)2541-2578
Number of pages38
JournalJournal of Functional Analysis
Volume260
Issue number9
DOIs
Publication statusPublished - 2011 May 1
Externally publishedYes

Keywords

  • Doubly nonlinear equations
  • Variational principle
  • Γ-convergence

ASJC Scopus subject areas

  • Analysis

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