Elliptic equations involving the 1-Laplacian and a subcritical source term

DOI10.1016/j.na.2017.11.006zbMath1391.35168arXiv1707.01934OpenAlexW2964094825MaRDI QIDQ681972

Sergio Segura de León, Alexis Molino Salas

Publication date: 13 February 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.01934

zbMATH Keywords

Dirichlet problem\(p\)-Laplacian1-Laplaciansubcritical source term

Mathematics Subject Classification ID

Variational methods for second-order elliptic equations (35J20) Singular elliptic equations (35J75) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (20)

Monotonicity and symmetry of positive solution for 1-Laplace equation ⋮ A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator ⋮ Existence of solution for a class of heat equation involving the 1-Laplacian operator ⋮ Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity ⋮ A Berestycki–Lions type result for a class of problems involving the 1-Laplacian operator ⋮ The existence of solutions for parabolic problem with the limiting case of double phase flux ⋮ Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator ⋮ Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator ⋮ Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities ⋮ On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity ⋮ On 1-Laplacian elliptic problems involving a singular term and an \(L^1\)-data ⋮ Existence and uniqueness of solution for some time fractional parabolic equations involving the 1-Laplace operator ⋮ Dirichlet or Neumann problem for weighted 1-Laplace equation with application to image denoising ⋮ On some weighted 1-Laplacian problem on \(\mathbb{R}^N\) with singular behavior at the origin ⋮ Anisotropic 1-Laplacian problems with unbounded weights ⋮ The Dirichlet problem for singular elliptic equations with general nonlinearities ⋮ Existence of a BV solution for a mean curvature equation ⋮ Multiplicity of solutions for a class of quasilinear problems involving the \(1\)-Laplacian operator with critical growth ⋮ The Dirichlet problem for the 1-Laplacian with a general singular term and L ¹-data ⋮ Multiple ordered solutions for a class of problems involving the 1-Laplacian operator

Cites Work

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• Pairings between measures and bounded functions and compensated compactness
• On some nonlinear equation involving the 1-Laplacian and trace map inequalities
• Parabolic quasilinear equations minimizing linear growth functionals
• Some qualitative properties for the total variation flow
• Existence theorems for equations involving the 1-Laplacian: first eigenvalues for \(-\Delta_1\)
• Behaviour of \(p\)-Laplacian problems with Neumann boundary conditions when \(p\) goes to \(1\)
• Dual variational methods in critical point theory and applications
• On a familiy of torsional creep problems.
• On Some Nonlinear Partial Differential Equations Involving the “1”-Laplacian and Critical Sobolev Exponent
• The Dirichlet problem for the total variation flow
• Variational and topological methods for Dirichlet problems with \(p\)-Laplacian
• Existence and uniqueness of a solution for a parabolic quasilinear problem for linear growth functionals with \(L^1\) data.
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