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Stationary Quasivariational Inequalities with Gradient Constraint and Nonhomogeneous Boundary Conditions

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From Particle Systems to Partial Differential Equations

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 75))

Abstract

We study existence of solution of stationary quasivariational inequalities with gradient constraint and nonhomogeneous boundary condition of Neumann or Dirichlet type. Through two different approaches, one making use of a fixed point theorem and the other using a process of regularization and penalization, we obtain different sufficient conditions for the existence of solution.

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Acknowledgements

The authors are grateful to the referees for valuable comments and suggestions that helped to improve the text.

This research was partially supported by CMAT – “Centro de Matemática da Universidade do Minho”, financed by FEDER Funds through “Programa Operacional Factores de Competitividade – COMPETE” and by Portuguese Funds through FCT, “Fundação para a Ciência e a Tecnologia”, within the Project Est-C/MAT/UI0013/2011.

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Authors and Affiliations

  1. CMAT and DMA, University of Minho, Braga, Portugal

    Assis Azevedo, Fernando Miranda & Lisa Santos

Authors
  1. Assis Azevedo
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  2. Fernando Miranda
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  3. Lisa Santos
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Corresponding author

Correspondence to Assis Azevedo .

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Editors and Affiliations

  1. UMR CNRS-UNS 7351, Université de Nice Sophia Antipolis, Laboratoire J.A.Dieudonné, Nice, France

    Cédric Bernardin

  2. Universidade do Minho, Centre of Mathematics, Braga, Portugal

    Patricia Gonçalves

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Azevedo, A., Miranda, F., Santos, L. (2014). Stationary Quasivariational Inequalities with Gradient Constraint and Nonhomogeneous Boundary Conditions. In: Bernardin, C., Gonçalves, P. (eds) From Particle Systems to Partial Differential Equations. Springer Proceedings in Mathematics & Statistics, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54271-8_2

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