Bounded solutions to the 1-Laplacian equation with a total variation term

DOI10.1007/S11587-018-0425-5zbMath1433.35089OpenAlexW2897598412WikidataQ129082326 ScholiaQ129082326MaRDI QIDQ2281538

Andrea Dall'Aglio, Sergio Segura de León

Publication date: 3 January 2020

Published in: Ricerche di Matematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11587-018-0425-5

zbMATH Keywords

nonlinear elliptic problems1-Laplacian operatorproblems with critical growth in the gradienttotal variation term as reaction

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (5)

1-Laplacian type problems with strongly singular nonlinearities and gradient terms ⋮ Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator ⋮ On 1-Laplacian elliptic problems involving a singular term and an \(L^1\)-data ⋮ Dirichlet or Neumann problem for weighted 1-Laplace equation with application to image denoising ⋮ Multiplicity of solutions to elliptic problems involving the 1-Laplacian with a critical gradient term

Cites Work

• Unnamed Item
• Unnamed Item
• Multiplicity of solutions to elliptic problems involving the 1-Laplacian with a critical gradient term
• On the entropy conditions for some flux limited diffusion equations
• On the solutions to 1-Laplacian equation with \(L^1\) data
• Pairings between measures and bounded functions and compensated compactness
• \(L^{\infty}\)-estimates for nonlinear elliptic problems with \(p\)-growth in the gradient
• Divergence-measure fields and hyperbolic conservation laws
• Parabolic quasilinear equations minimizing linear growth functionals
• Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small
• Anzellotti's pairing theory and the Gauss-Green theorem
• Existence and comparison results for an elliptic equation involving the 1-Laplacian and \(L^1\)-data
• Nonlinear elliptic equations with natural growth in the gradient and source terms in Lorentz spaces
• Nonlinear elliptic equations with natural growth in general domains
• Bounded solutions to the 1-Laplacian equation with a critical gradient term
• Weakly Differentiable Functions
• $L^\infty $ Estimate for Some Nonlinear Elliptic Partial Differential Equations and Application to an Existence Result
• On Some Nonlinear Partial Differential Equations Involving the “1”-Laplacian and Critical Sobolev Exponent
• The Dirichlet problem for the total variation flow

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