1,721,040 research outputs found
A note on the paper "Optimizing improved Hardy inequalities" by S. Filippas and A. Tertikas
No full textIn this short note we prove that Theorem A in
[S. Filippas - A. Tertikas},
{Optimizing Improved Hardy Inequalities},
J. Funct. Analysis 192 (2002) 186-233] is incorrect
Existence of extremals for the Maz'ya and for the Caffarelli-Kohn-Nirenberg inequalities
No full textThis paper deals with some Sobolev-type inequalities with weights that were proved by Maz'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984
Existence and multiplicity results for a weighted p-Laplace equation involving Hardy potentials and critical nonlinearities.
No full textWe study a class of elliptic problems involving
weighted -Laplace operators, critical growths and Hardy potentials.
The main motivation lies in some Hardy-Sobolev type inequalities
that were proved by Caffarelli-Kohn-Nirenberg
in 1984
On the regularity of weak solutions to H-systems
No full textWe prove that every weak solution to the H-surface equation is locally bounded, provided the prescribed mean curvature H satisfies a suitable condition at infinity. No smoothness assumption is required on H. We also consider the Dirichlet problem for the H-surface equation on a bounded regular domain with bounded
boundary data and the H-bubble problem. Under the same assumptions on H, we prove that every weak solution is globally bounded
OPTIMAL RELLICH-SOBOLEV CONSTANTS AND THEIR EXTREMALS
No full textWe prove that extremals for second order Rellich-Sobolev
inequalities have a constant sign. Then, we show that the optimal con-
stants in Rellich-Sobolev inequalities on a bounded domain
and under Navier boundary conditions do not depend on Ω
Ground state solutions of a critical problem involving cylindrical weights
No full textWe prove some existence and non-existence results for a nonlinear elliptic equation involving cylindrical weights and critical growth
Weighted Sobolev spaces of radially symmetric functions
No full textWe prove dilation invariant inequalities involving radial functions, poliharmonic
operators and weights that are powers of the distance from the origin. Then, we discuss the
existence of extremals, and in some cases, we compute the best constants
Multiple positive solutions of a scalar field equation in R^n
No full textFrom the viewpoint of the calculus of variations, the perturbed Kazdan-Warner problem:
(1) −∆u+λu=k(x)u^{p−1}, u>0 in R^n, u→0 at ∞,
where n≥3 and p>1 is subcritical. Problem (1) is studied with regard of the effect of the set M on topology of the energy sub levels: in the main results it is shown that the Lyusternik-Schnirelman category of M can
affect the number of positive solutions to (1) in case p is close enough to the critical Sobolev exponent
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