NDLI: Hardy inequalities resulted from nonlinear problems dealing with A-Laplacian

Content Provider	SpringerLink
Author	Skrzypczak, Iwona
Copyright Year	2014
Abstract	We derive Hardy inequalities in weighted Sobolev spaces via anticoercive partial differential inequalities of elliptic type involving A-Laplacian −Δ A u = −divA(∇u) ≥ Φ, where Φ is a given locally integrable function and u is defined on an open subset $${\Omega \subseteq \mathbb{R}^n}$$ . Knowing solutions we derive Caccioppoli inequalities for u. As a consequence we obtain Hardy inequalities for compactly supported Lipschitz functions involving certain measures, having the form $$\int_\Omega F_{\bar{A}}(\|\xi\|) \mu_1(dx) \leq \int_\Omega \bar{A}(\|\nabla \xi\|)\mu_2(dx),$$ where $${\bar{A}(t)}$$ is a Young function related to A and satisfying Δ′-condition, while $${F_{\bar{A}}(t) = 1/(\bar{A}(1/t))}$$ . Examples involving $${\bar{A}(t) = t^p{\rm log}^\alpha(2+t), p \geq 1, \alpha \geq 0}$$ are given. The work extends our previous work (Skrzypczaki, in Nonlinear Anal TMA 93:30–50, 2013), where we dealt with inequality −Δ p u ≥ Φ, leading to Hardy and Hardy–Poincaré inequalities with the best constants.
Ending Page	868
Page Count	28
Starting Page	841
File Format	PDF
ISSN	10219722
e-ISSN	14209004
Journal	Nonlinear Differential Equations and Applications NoDEA
Issue Number	6
Volume Number	21
Language	English
Publisher	Springer Basel
Publisher Date	2014-04-16
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Inequalities involving derivatives and differential and integral operators Orlicz–Sobolev spaces Weak solutions Partial differential inequalities A-harmonic PDEs Nonlinear eigenvalue problems Analysis Nonlinear elliptic equations Harmonic, subharmonic, superharmonic functions Hardy-type estimates
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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