322,963 research outputs found
Asymptotics of the s-perimeter as s ↘ 0
No full textWe deal with the asymptotic behavior of the s-perimeter of a set E inside a domain Omega as s SE arrow 0. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of E and Omega. Moreover, we construct examples of sets for which the limit does not exist
Asymptotics of fractional perimeter functionals and related problems
No full textIn this paper we review some recent results concerning the asymptotics of a fractional perimeter and the regularity of the corresponding minimizers. We also provide an elementary example of set with infinite s-perimeter
Is the ascorbate system involved in the induction of the oxidative burst by oligogalacturonides and salicylic acid?
No full textBologn
Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains
No full textAbstractWe consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain Ω⊂Rn whose boundary has an (n−2)-dimensional singularity. Assuming 1<p<n+2n−2, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero
Hardy inequalities on Riemannian manifolds and applications
No full textWe prove a simple sufficient criteria to obtain some Hardy inequalities on Rie-
mannian manifolds related to quasilinear second-order differential operator ∆p u :=
div | u|p−2 u . Namely, if ρ is a nonnegative weight such that −∆p ρ ≥ 0, then
the Hardy inequality
c M
|u|p
| ρ|p dvg ≤
ρp
| u|p dvg ,
∞
u ∈ C0 (M ).
M
holds. We show concrete examples specializing the function ρ.
Our approach allows to obtain a characterization of p-hyperbolic manifolds as
well as other inequalities related to Caccioppoli inequalities, weighted Gagliardo-
Nirenberg inequalities, uncertain principle and first order Caffarelli-Kohn-Nirenberg
interpolation inequality
Purification and characterization of an ascorbate peroxidase from potato tuber mitochondria
No full textGeometric inequalities and symmetry results for elliptic systems
No full textWe obtain some Poincaré type formulas, that we use, together with the level set analysis, to detect the one-dimensional symmetry of monotone and stable solutions of possibly degenerate elliptic systems of the form div (a (jruj)ru) = F1(u; v); div (b (jrvj)rv) = F2(u; v); where F 2 C1;1 loc (R2). Our setting is very general, and it comprises, as a particular case, a conjec- ture of De Giorgi for phase separations in R2
On a fractional harmonic replacement
No full textGiven s ∈ (0, 1), we consider the problem of minimizing the fractional Gagliardo seminorm in Hs with prescribed condition outside the ball and under the further constraint of attaining zero value in a given set K. We investigate how the energy changes in dependence of such set. In particular, under mild regularity conditions, we show that adding a set A to K increases the energy of at most the measure of A (this may be seen as a perturbation result for small sets A). Also, we point out a monotonicity feature of the energy with respect to the prescribed sets and the boundary conditions
Isolation and characterization of a novel aquaporin in pumpkin (Cucurbita Pepo L.) roots
No full text- …
