Nonstandard growth optimization problems with volume constraint.

ARIEL SALORT; SCHVAGER, BELEM B.; ANALÍA SILVA

DIFFERENTIAL AND INTEGRAL EQUATIONS

Khayyam Publishing

Año: 2023 vol. 36

0893-4983

In this article we study some optimal design problems relatedto nonstandard growth eigenvalues ruled by the g−Laplacian operator.More precisely, given Ω ⊂ Rn and α, c > 0 we consider the optimizationproblem inf{λΩ(α,E) : E ⊂ Ω, |E| = c}, where λΩ(α,E) is related tothe first eigenvalue to−div(g(|∇u|) ∇u/|∇u| ) + g(u) u/|u| + αχEg(u) u/|u| in Ωsubject to Dirichlet, Neumann or Steklov boundary conditions.We analyze existence of an optimal configuration, symmetry propertiesof them, and the asymptotic behavior as α approaches +∞.