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A quasilinear eigenvalue problem with Robin conditions on the non-smooth domain of finite measure. (English) Zbl 1202.35149

Summary: We consider a nonlinear eigenvalue problem involving the \(p\)-Laplacian with Robin boundary conditions on a domain of finite measure. We show existence, simplicity and isolation of the principal eigenvalue and regularity results for the corresponding eigenfunction. Furthermore, we establish the link between the Dirichlet and Neumann problems by means of the Robin boundary conditions with variable parameter.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J25 Boundary value problems for second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
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