The eigenvalue problem for the 1-biharmonic operator

DOI10.2422/2036-2145.201106_013zbMath1308.46047OpenAlexW4299682965MaRDI QIDQ5169957

Bernhard Ruf, Enea Parini, Cristina Tarsi

Publication date: 16 July 2014

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2422/2036-2145.201106_013

zbMATH Keywords

Sobolev spacesfirst eigenvalueconvex domainFaber-Krahn inequalitydistributional solutionnon-smooth analysistorsion function1-biharmonic operator

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Boundary value problems for linear higher-order PDEs (35G15)

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A remark on the first \(p\)-buckling eigenvalue with an adhesive constraint ⋮ Existence of nontrivial solution for quasilinear equations involving the 1-biharmonic operator ⋮ Higher-order functional inequalities related to the clamped 1-biharmonic operator ⋮ Existence and concentration properties for the 1-biharmonic equation with lack of compactness ⋮ The eigenvalue problem for the \(\infty \)-Bilaplacian ⋮ Some existence results of bounded variation solutions for a 1‐biharmonic problem with vanishing potentials ⋮ Existence and concentration of solutions for a 1-biharmonic Choquard equation with steep potential Well in \(R^N \) ⋮ Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions ⋮ Some existence results of bounded variation solutions to 1-biharmonic problems ⋮ Properties of the 1-polyharmonic operator in the whole space and applications to nonlinear elliptic equations ⋮ On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result ⋮ Existence and uniqueness of weak solutions for some singular evolutionary system in image denoising

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