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Γ-convergence of the energy functionals for the variable exponent p(·)-Laplacian and stability of the minimizers with respect to integrability

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Abstract

We investigate the non-homogeneous modular Dirichlet problem Δ p (·)u(x) = f (x) (where Δ p (·)u(x) = div(|∇u|p(x-2)∇u(x)) from the functional analytic point of view and we prove the stability of the solutions \({\left( {{u_{{p_i}}}} \right)_i}\) of the equation \({\Delta _{{p_i}\left( \cdot \right)}}{u_{{p_i}\left( \cdot \right)}} = f\) as p i (·) → q(·) via Gamma-convergence of sequence of appropriate functionals.

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Authors and Affiliations

  1. Department Of Mathematical Sciences, Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210-1174, USA

    Jan Lang

  2. Department of Mathematical Sciences, University of Texas at El Paso, 500 W University Ave., El Paso, TX, 79968, USA

    Osvaldo Méndez

Authors
  1. Jan Lang
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  2. Osvaldo Méndez
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Correspondence to Jan Lang.

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Lang, J., Méndez, O. Γ-convergence of the energy functionals for the variable exponent p(·)-Laplacian and stability of the minimizers with respect to integrability. JAMA 134, 575–596 (2018). https://doi.org/10.1007/s11854-018-0018-y

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  • DOI: https://doi.org/10.1007/s11854-018-0018-y

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