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In this paper we classify all positive extremal functions to a sharp weighted Sobolev inequality on the upper half space, which involves divergent operators with degeneracy on the boundary. As an application of the results, we can derive a sharp Sobolev type inequality involving Baouendi-Grushin operator, and classify certain extremal functions for all $tau>0$ and $m e2 $ or $ n e1$.
We prove the sharp quantitative stability for a wide class of weighted isoperimetric inequalities. More precisely, we consider isoperimetric inequalities in convex cones with homogeneous weights. Inspired by the proof of such isoperimetric inequali
We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A general method
The sharp trace inequality of Jose Escobar is extended to traces for the fractional Laplacian on R^n and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Liebs sharp form of the Hardy-Littlewood-Sobolev inequality.
Let $M$ be a complete, simply connected Riemannian manifold with negative curvature. We obtain some Moser-Trudinger inequalities with sharp constants on $M$.
This paper presents a highly non-trivial two-fold study of the fractional differential couples - derivatives ($ abla^{0<s<1}_+=(-Delta)^frac{s}{2}$) and gradients ($ abla^{0<s<1}_-= abla (-Delta)^frac{s-1}{2}$) of basic importance in the theory of fr