Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions
We consider a class of equations in divergence form with a singular/degenerate weight− div
(| y| a A (x, y)∇ u)=| y| af (x, y) or div (| y| a F (x, y)). Under suitable regularity assumptions for …
(| y| a A (x, y)∇ u)=| y| af (x, y) or div (| y| a F (x, y)). Under suitable regularity assumptions for …
Uniform bounds for strongly competing systems: the optimal Lipschitz case
For a class of systems of semi-linear elliptic equations, including-Δ u_i= f_i (x, u_i)-β u_i j ≠ i
a_ ij u_j^ p,\quad i= 1,\dots, k,-Δ ui= fi (x, ui)-β ui∑ j≠ iaijujp, i= 1,⋯, k, for p= 2 (variational …
a_ ij u_j^ p,\quad i= 1,\dots, k,-Δ ui= fi (x, ui)-β ui∑ j≠ iaijujp, i= 1,⋯, k, for p= 2 (variational …
Uniform H\" older regularity with small exponent in competition-fractional diffusion systems
For a class of competition-diffusion nonlinear systems involving fractional powers of the
Laplacian, including as a special case the fractional Gross-Pitaevskii system, we prove that …
Laplacian, including as a special case the fractional Gross-Pitaevskii system, we prove that …
A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian
S Dipierro, A Pinamonti - Journal of Differential Equations, 2013 - Elsevier
We study the symmetry properties for solutions of elliptic systems of the type where F∈
Cloc1, 1 (R2), s1, s2∈(0, 1) and the operator (− Δ) s is the so-called fractional Laplacian. We …
Cloc1, 1 (R2), s1, s2∈(0, 1) and the operator (− Δ) s is the so-called fractional Laplacian. We …
On s-harmonic functions on cones
On s-harmonic functions on cones Page 1 ANALYSIS & PDE msp Volume 11 No. 7 2018
SUSANNA TERRACINI, GIORGIO TORTONE AND STEFANO VITA ON s-HARMONIC …
SUSANNA TERRACINI, GIORGIO TORTONE AND STEFANO VITA ON s-HARMONIC …
A Liouville type theorem for Lane–Emden systems involving the fractional Laplacian
We establish a Liouville type theorem for the fractional Lane–Emden system:{(− Δ) αu= vqin
RN,(− Δ) αv= upin RN, where $\alpha\in (0, 1) $, $ N> 2\alpha $ and p, q are positive real …
RN,(− Δ) αv= upin RN, where $\alpha\in (0, 1) $, $ N> 2\alpha $ and p, q are positive real …
Concentration phenomena for critical fractional Schr\" odinger systems
V Ambrosio - arXiv preprint arXiv:1704.04391, 2017 - arxiv.org
In this paper we study the existence, multiplicity and concentration behavior of solutions for
the following critical fractional Schr\" odinger system\begin {equation*}\left\{\begin …
the following critical fractional Schr\" odinger system\begin {equation*}\left\{\begin …
On the nodal set of solutions to degenerate or singular elliptic equations with an application to s-harmonic functions
This work is devoted to the geometric-theoretic analysis of the nodal set of solutions to
degenerate or singular equations involving a class of operators including L a= div (| y| a∇) …
degenerate or singular equations involving a class of operators including L a= div (| y| a∇) …
Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping
We study interior regularity issues for systems of elliptic equations of the type− Δ ui= fi, β (x)−
β∑ j≠ iaijui| ui| p− 1| uj| p+ 1 set in domains Ω⊂ RN, for N⩾ 1. The paper is devoted to the …
β∑ j≠ iaijui| ui| p− 1| uj| p+ 1 set in domains Ω⊂ RN, for N⩾ 1. The paper is devoted to the …
On isolated singularities of fractional semi-linear elliptic equations
H Yang, W Zou - Annales de l'Institut Henri Poincaré C, Analyse non …, 2021 - Elsevier
In this paper, we study the local behavior of nonnegative solutions of fractional semi-linear
equations (− Δ) σ u= up with an isolated singularity, where σ∈(0, 1) and nn− 2 σ< p< n+ 2 σ …
equations (− Δ) σ u= up with an isolated singularity, where σ∈(0, 1) and nn− 2 σ< p< n+ 2 σ …