Sharp gradient stability for the Sobolev inequality Page 1 SHARP GRADIENT STABILITY FOR
THE SOBOLEV INEQUALITY ALESSIO FIGALLI and YI RU-YA ZHANG Abstract We prove a …

This paper is devoted to considering the following Hardy-Sobolev inequality\[\int_ {\mathbb
{R}^ N}|\nabla u|^ p\mathrm {d} x\geq\mathcal {S} _\beta\left (\int_ {\mathbb {R}^ N}\frac …

We derive Hardy inequalities in weighted Sobolev spaces via anticoercive partial differential
inequalities of elliptic type involving A-Laplacian− Δ A u=− div A (∇ u)≥ Φ, where Φ is a …

We obtain Caccioppoli-type estimates for nontrivial and nonnegative solutions to
anticoercive partial differential inequalities of elliptic type involving weighted p-Laplacian:-Δ …

We investigate nonexistence of nonnegative solutions to a partial differential inequality
involving the p (x)–Laplacian of the form−∆ p (x) u≥ Φ (x, u (x),∇ u (x)) in Rn, as well as in …

We study weighted inequalities of Hardy and Hardy–Poincaré type and find necessary and
sufficient conditions on the weights so that the considered inequalities hold. Examples with …

We obtain Caccioppoli--type estimates for nontrivial and nonnegative solutions to the
anticoercive partial differential inequalities of elliptic type involving degenerated $ p …

We apply the recent method of Drábek and the authors in order to construct the Hardy–
Poincaré–type inequalities ̄ C _ γ, n, p, r ∫ _ R^ n ‖ ξ|^ p\left (1+ r| x|^ p p-1\right)\left (1+ …

We derive a family of weighted Hardy-type inequalities in the variable exponent Lebesgue
space with an additional term of the form\[\int_\Omega\|\xi|^{p (x)}\mu_ {1,\beta}(dx)\leqslant …

Our purpose is to give the new constructive method of derivation of Hardy and Hardy–
Sobolev inequalities. We build inequalities knowing solutions u to p and A–harmonic …