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On Some Variable Exponent Problems with No-Flux Boundary Condition

  • Maria-Magdalena Boureanu
Chapter

Abstract

The variable exponent problems allow us to deal with nonhomogeneous materials for which it is not suitable to use the functional framework provided by the Lebesgue and Sobolev-type spaces with constant exponents. The no-flux boundary condition first appeared in physics and it opens the door to more real-life applications. In addition to the no-flux boundary condition, our problems involve more general operators, that is, Leray–Lions type operators. The discussion is centered on the weak solvability of such problems via the critical point theory, and it also includes the case of anisotropic exponents. For a plus of cohesion, we select only a few powerful theorems as main tools that can be applied to all these problems.

Keywords

Variable exponent spaces Anisotropic exponent Nonlinear elliptic problems No-flux boundary condition Leray–Lions type operators Weak solutions Existence Multiplicity 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maria-Magdalena Boureanu
    • 1
  1. 1.Department of Applied MathematicsUniversity of CraiovaCraiovaRomania

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