On Some Variable Exponent Problems with No-Flux Boundary Condition

Maria-Magdalena Boureanu ()
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Maria-Magdalena Boureanu: University of Craiova, Department of Applied Mathematics

Chapter Chapter 9 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 253-285 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-15242-0_9

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DOI: 10.1007/978-3-030-15242-0_9

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