On one variant of strongly nonlinear Gagliardo–Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problems

  • Tomasz Choczewski

    University of Warsaw, Poland
  • Agnieszka Kalamajska

    University of Warsaw, Poland and Polish Academy of Sciences, Warsaw, Poland
On one variant of strongly nonlinear Gagliardo–Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problems cover
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Abstract

We obtain the inequality

where is a bounded Lipschitz domain, is positive and obeys some additional assumptions, is the Laplace operator, is certain transformation of the continuous function . We also explain how to apply such inequality to deduce regularity for solutions of nonlinear eigenvalue problems of elliptic type for degenerated PDEs, with the illustration within the model of electrostatic micromechanical systems (MEMS).

Cite this article

Tomasz Choczewski, Agnieszka Kalamajska, On one variant of strongly nonlinear Gagliardo–Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 3, pp. 479–496

DOI 10.4171/RLM/856