On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result

DOI10.1051/cocv/2020011zbMath1460.35169OpenAlexW3011680856MaRDI QIDQ5854378

E. Juárez Hurtado, Marcos T. O. Pimenta, Olímpio Hiroshi Miyagaki

Publication date: 17 March 2021

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/cocv/2020011

zbMATH Keywords

Poisson equationcompactness of the embeddingsquasilinear elliptic problem of higher-order

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Higher-order elliptic equations (35J30) Variational methods for higher-order elliptic equations (35J35) Quasilinear elliptic equations (35J62) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (5)

Existence of nontrivial solution for quasilinear equations involving the 1-biharmonic operator ⋮ Existence and concentration properties for the 1-biharmonic equation with lack of compactness ⋮ 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 \(R^N \) ⋮ Properties of the 1-polyharmonic operator in the whole space and applications to nonlinear elliptic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
• Lions-type compactness and Rubik actions on the Heisenberg group
• Limiting Sobolev inequalities and the 1-biharmonic operator
• On Palais' principle for non-smooth functionals
• Anisotropic \(p,q\)-Laplacian equations when \(p\) goes to 1
• Best constants in a borderline case of second-order Moser type inequalities
• Higher-order functional inequalities related to the clamped 1-biharmonic operator
• On the solutions to 1-Laplacian equation with \(L^1\) data
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• On a class of nonlinear Schrödinger equations
• Existence of solitary waves in higher dimensions
• Parabolic quasilinear equations minimizing linear growth functionals
• Existence theorems for equations involving the 1-Laplacian: first eigenvalues for \(-\Delta_1\)
• Strauss' and Lions' type results in \(BV(\mathbb R^N)\) with an application to an 1-Laplacian problem
• On existence and concentration of solutions to a class of quasilinear problems involving the 1-Laplace operator
• Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials
• 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
• Minimizing total variation flow
• The principle of symmetric criticality for non-differentiable mappings
• Functions of least gradient and 1-harmonic functions
• Variational Analysis in Sobolev andBVSpaces
• DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM
• KATO'S INEQUALITY UP TO THE BOUNDARY
• The Euler Equation for Functionals with Linear Growth
• Generalized Gradients and Applications
• Minimizing total variation flow
• The Dirichlet problem for a singular elliptic equation arising in the level set formulation of the inverse mean curvature flow
• The eigenvalue problem for the 1-biharmonic operator
• The Dirichlet problem for the total variation flow

This page was built for publication: On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result