ASYMPTOTIC BEHAVIOUR OF MINIMIZING SEQUENCES FOR HARDY'S INEQUALITY

DOI10.1142/S0219199700000098zbMath0956.35036OpenAlexW2019749246MaRDI QIDQ4513341

Itai Shafrir

Publication date: 14 November 2000

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199700000098

zbMATH Keywords

strong convergenceminimizing sequencesbest constantHardy's inequality

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) PDEs with low regular coefficients and/or low regular data (35R05) Inequalities for sums, series and integrals (26D15)

Related Items (16)

Positive solutions to nonlinear \(p\)-Laplace equations with Hardy potential in exterior domains ⋮ Existence and regularity of positive solutions of elliptic equations of Schrödinger type ⋮ Best constants in bipolar \(L^p\) Hardy-type inequalities ⋮ Asymptotic behaviour of the first eigenfunction of a Hardy-Sobolev operator. ⋮ The Douglas formula in \(L^p\) ⋮ Hardy inequalities for magnetic p-Laplacians ⋮ On minimization problems which approximate Hardy \(L^{p}\) inequality. ⋮ Unnamed Item ⋮ A Liouville-type theorem for the \(p\)-Laplacian with potential term ⋮ Uniqueness of positive solutions for singular problems involving the $p$-Laplacian ⋮ Groundstate asymptotics for a class of singularly perturbed \(p\)-Laplacian problems in \({{\mathbb{R}}}^N\) ⋮ Nonlinear elliptic problem related to the Hardy inequality with singular term at the boundary ⋮ Positive solutions of the \(p\)-Laplacian involving a superlinear nonlinearity with zeros ⋮ On the Fučik spectrum of Hardy-Sobolev operator ⋮ Some improved Caffarelli-Kohn-Nirenberg inequalities ⋮ A semilinear parabolic problem with singular term at the boundary

Cites Work

• Regularity for a more general class of quasilinear equations
• Maximum and anti-maximum principles and eigenfunctions estimates via perturbation theory of positive solutions of elliptic equations
• Extremal functions for Hardy's inequality with weight
• Local behavior of solutions of quasi-linear equations
• The best possible constant in generalized Hardy's inequality for convex domain in rn
• Remarks on sublinear elliptic equations
• On the best constant for Hardy’s inequality in $\mathbb {R}^n$
• A Picone's identity for the p-Laplacian and applications
• THE HARDY CONSTANT

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