Capacitary strong type estimates in semilinear problems

DOI10.5802/aif.1251zbMath0741.35012OpenAlexW2035461292MaRDI QIDQ1175681

S. Singh

Publication date: 25 June 1992

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1991__41_1_117_0

zbMATH Keywords

Sobolev spacesexistenceremovable setsclass of weak solutions

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Nonlinear elliptic equations (35J60) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (23)

Some remarks on elliptic problems with critical growth in the gradient ⋮ Nonlinear equations and weighted norm inequalities ⋮ Nonlinear elliptic systems with coupled gradient terms ⋮ Boundary singular solutions of a class of equations with mixed absorption-reaction ⋮ Sharp \(L^ p\)-weighted Sobolev inequalities ⋮ Capacitary inequalities for fractional integrals, with applications to partial differential equations and Sobolev multipliers ⋮ Stationary Navier-Stokes equations with critically singular external forces: existence and stability results ⋮ Quasilinear and Hessian Lane-Emden type systems with measure data ⋮ Potential Estimates and Quasilinear Parabolic Equations with Measure Data ⋮ Wiener regularity for large solutions of nonlinear equations ⋮ Removable singularities and singular solutions of semilinear elliptic equations ⋮ On strong solvability of the Dirichlet problem for a class of semilinear elliptic equations with discontinuous coefficients ⋮ A generalization of a criterion for the existence of solutions to semilinear elliptic equations ⋮ Conductor and capacitary inequalities for functions on topological spaces and their applications to Sobolev-type imbeddings ⋮ Conductor inequalities and criteria for Sobolev type two-weight imbeddings ⋮ Quasilinear Riccati Type Equations with Super-Critical Exponents ⋮ Quasilinear and Hessian type equations with exponential reaction and measure data ⋮ Singular quasilinear and Hessian equations and inequalities ⋮ Conductor Inequalities and Criteria for Sobolev-Lorentz Two-Weight Inequalities ⋮ A capacity-based condition for existence of solutions to fractional elliptic equations with first-order terms and measures ⋮ Local Integral Estimates and Removable Singularities for Quasilinear and Hessian Equations with Nonlinear Source Terms ⋮ Quasilinear equations with source terms on Carnot groups ⋮ Existence results for semilinear elliptic equations with small measure data

Cites Work

• Singularités éliminables pour des équations semi-linéaires
• Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations)
• On the existence of capacitary strong type estimates in \(R^n\)
• Imbedding theorems of Sobolev type in potential theory.
• Weighted norm inequalities for maximal functions and singular integrals
• On Certain Convolution Inequalities
• Weighted Norm Inequalities for the Hardy Maximal Function
• A Theory of Capacities for Potentials of Functions in Lebesgue Classes.
• The Equivalence of Two Definitions of Capacity
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