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Some characterizations of magnetic Sobolev spaces
ABSTRACT The 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]; NguyenExpand
A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian
We study the symmetry properties for solutions of elliptic systems of the type (-\Delta)^{s_1} u = F_1(u, v), (-\Delta)^{s_2} v= F_2(u, v), where $F\in C^{1,1}_{loc}(\R^2)$, $s_1,s_2\in (0,1)$ andExpand
Poincaré-type inequality for Lipschitz continuous vector fields
Abstract The scope of this paper is to prove a Poincare type inequality for a family of nonlinear vector fields, whose coefficients are only Lipschitz continuous with respect to the distance inducedExpand
Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions
We consider a boundary value problem driven by the p-fractional Laplacian with nonlocal Robin boundary conditions and we provide necessary and sufficient conditions which ensure the existence of aExpand
Weighted Sobolev Spaces on Metric Measure Spaces
We investigate weighted Sobolev spaces on metric measure spaces $(X,d,m)$. Denoting by $\rho$ the weight function, we compare the space $W^{1,p}(X,d,\rho m)$ (which always concides with the closureExpand
A Lewy-Stampacchia estimate for variational inequalities in the Heisenberg group
We consider an obstacle problem in the Heisenberg group framework, and we prove that the operator on the obstacle bounds point- wise the operator on the solution. More explicitly, if ¯ u minimizesExpand
Rigidity results for elliptic boundary value problems: stable solutions for quasilinear equations with Neumann or Robin boundary conditions
We provide a general approach to the classification results of stable solutions of (possibly nonlinear) elliptic problems with Robin conditions. The method is based on a geometric formula ofExpand
The Maz'ya-Shaposhnikova limit in the magnetic setting
We prove a magnetic version of the Maz'ya-Shaposhnikova singular limit of nonlocal norms with vanishing fractional parameter. This complements a general convergence result recently obtained byExpand
Multiplicity results for magnetic fractional problems
Abstract The paper deals with the existence of multiple solutions for a boundary value problem driven by the magnetic fractional Laplacian ( − Δ ) A s , that is ( − Δ ) A s u = λ f ( | u | ) u  in  ΩExpand
Magnetic BV-functions and the Bourgain–Brezis–Mironescu formula
Abstract We prove a general magnetic Bourgain–Brezis–Mironescu formula which extends the one obtained in [37] in the Hilbert case setting. In particular, after developing a rather complete theory ofExpand