1,721,017 research outputs found
Some characterizations of magnetic Sobolev spaces
Full text linkThe aim of this note is to survey recent results contained in Nguyen H-M, Squassina M. [On anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI:10.1142/S0219199718500177]; Nguyen H-M, Pinamonti A, Squassina M, et al. [New characterizations of magnetic Sobolev spaces. Adv Nonlinear Anal. 2018;7(2):227–245]; Pinamonti A, Squassina M, Vecchi E. [Magnetic BV functions and the Bourgain-Brezis-Mironescu formula. Adv Calc Var, to appear. DOI:10.1515/acv-2017-0019]; Pinamonti A, Squassina M, Vecchi E. [The Maz'ya-Shaposhnikova limit in the magnetic setting. J Math Anal Appl. 2017;449:1152–1159] and Squassina M, Volzone B. [Bourgain-Brezis-Mironescu formula for magnetic operators. C R Math Acad Sci Paris. 2016;354:825–831], where the authors extended to the magnetic setting several characterizations of Sobolev and BV functions
Ground states for fractional magnetic operators
No full textWe study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained via concentration compactness
Soliton dynamics for a general class of Schrodinger equations
No full textThe soliton dynamics for a general class of nonlinear focusing Schrodinger problems in presence of non-constant external (local and nonlocal) potentials is studied by taking as initial datum the ground state solution of ail associated autonomous elliptic equation. (C) 2009 Elsevier Inc. All rights reserved
Unbounded critical points for a class of lower semicontinuous functionals
No full textIn this paper we prove existence and multiplicity results of unbounded
critical points for a general class of weakly lower semicontinuous functionals.
We will apply a nonsmooth critical point theory developed
by Degiovanni et al. to treat the case of continuous functionals
On Coron's problem for the p-Laplacian
Full text linkWe prove that the critical problem for the p-Laplacian operator admits a nontrivial solution in annular shaped domains with sufficiently small inner hole. This extends Coron's result [4] to a class of quasilinear problems
Existence results for a doubly nonlocal equation
No full textIn this note we expose some results proved in d’Avenia et al. [8] concerning an elliptic problem in RN which involves two nonlocal operators: the fractional Laplacian and a convolution term of Hartree type. This equation has been called fractional Choquard equation. The results obtained concern regularity of weak solutions, existence and properties of ground states, as well as multiplicity and nonexistence of solutions
A note on global regularity for the weak solutions of fractional p-Laplacian equations
No full textWe consider a boundary value problem driven by the fractional p-Laplacian operator with a bounded reaction term. By means of barrier arguments, we prove Hölder regularity up to the boundary for the weak solutions, both in the singular (1 < p < 2) and the degenerate (p > 2) cas
Deformation from symmetry for Schrodinger equations of higher order on unbounded domains
No full textBy means of a perturbation method recently introduced by Bolle, we discuss the existence of infinitely many solutions for a class of perturbed symmetric higher order Schrodinger equations with non-homogeneous boundary data on unbounded domains
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