GROUP INVARIANCE AND POHOZAEV IDENTITY IN MOSER-TYPE INEQUALITIES

Pohozaev-type inequalities and their applications for elliptic equations

Fractional Laplacian: Pohozaev Identity and Nonexistence Results

In this note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semilinear problems with supercritical nonlinearities in starshaped domains. Résumé. Dans cette note, nous présentons l’identité de Pohozaev pour le Laplacien fractionnaire. Comme conséquence de cette identité, nous prouvons ...

Moser-Trudinger And Adams Type Inequalities And Their Applications

MOSER-TRUDINGER AND ADAMS TYPE INEQUALITIES AND THEIRAPPLICATIONSbyNGUYEN LAMAugust 2014Advisor: Dr. Guozhen LuMajor: MathematicsDegree: Doctor of PhilosophyIn this dissertation, we study some variants of the Moser-Trudinger inequalities and Adamsinequalities. The proofs of these inequalities relied crucially on the symmetrization arguments inthe lite...

The Pohozaev Identity for the Fractional Laplacian

In this paper we prove the Pohozaev identity for the semilinear Dirichlet problem (−∆)u = f(u) in Ω, u ≡ 0 in R\Ω. Here, s ∈ (0, 1), (−∆) is the fractional Laplacian in R, and Ω is a bounded C domain. To establish the identity we use, among other things, that if u is a bounded solution then u/δ|Ω is C up to the boundary ∂Ω, where δ(x) = dist(x, ∂Ω). In the fractional Pohozaev identity, the func...

On Trudinger-Moser type inequalities involving Sobolev-Lorentz spaces

Generalizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are related phenomena of co...