Uniqueness for fractional parabolic and elliptic equations with drift [PDF]
arXiv, 2022 We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.
arxiv
A note on the complete rotational invariance of biradial solutions to semilinear elliptic equations
, 2010 We investigate symmetry properties of solutions to equations of the form $$ -\Delta u = \frac{a}{|x|^2} u + f(|x|, u)$$ in R^N for $N \geq 4$, with at most critical nonlinearities.
Abatangelo, L., Terracini, S.
core +1 more source
$L^\infty$-bounds for general singular elliptic equations with convection term
, 2020 In this note we present $L^\infty$-results for problems of the form $A(x,u,Du)=B(x,u,Du)$ in $\Omega$, $u>0$ in $\Omega$, $u=0$ on $\partial\Omega$, where the growth condition for the function $B\colon \Omega \times \mathbb{R}\times \mathbb{R}^N\to ...
Marino, Greta, Winkert, Patrick
core +1 more source
Classification of solutions to $Δu = u^{-γ}$ in the half-space [PDF]
arXiv, 2023 We provide a classification result for positive solutions to $\Delta u = u^{-\gamma}$ in the half space, under zero Dirichlet boundary condition.
arxiv
Multiple Aharonov--Bohm eigenvalues: the case of the first eigenvalue on the disk
, 2018 It is known that the first eigenvalue for Aharonov--Bohm operators with half-integer circulation in the unit disk is double if the potential's pole is located at the origin. We prove that in fact it is simple as the pole $a\neq 0$
Abatangelo, Laura
core +1 more source
Structure Results for Semilinear Elliptic Equations with Hardy Potentials
Advanced Nonlinear Studies, 2018 We prove structure results for the radial solutions of the semilinear ...
Franca Matteo, Garrione Maurizio
doaj +1 more source
Convexity Property of Finsler Infinity Harmonic Functions
International Journal of Differential Equations, Volume 2024, Issue 1, 2024.In this paper, we investigate the convexity property of viscosity solutions to a homogeneous normalized Finsler infinity Laplacian equation. Weak and strong forms for convexity property have been addressed.
Benyam Mebrate, Sining Zheng
wiley +1 more source
The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity
, 2019 We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term.
Birindelli, Isabeau, Galise, Giulio
core +1 more source
Non-degeneracy of Gauss curvature equation with negative conic singularity [PDF]
Pacific J. Math. 297 (2018) 455-475, 2017 We study the Gauss curvature equation with negative singularities. For a local mean field type equation with only one negative index we prove a uniqueness property. For a global equation with one or two negative indexes we prove the non-degeneracy of the linearized equations.
arxiv +1 more source
On critical elliptic problems with singular Trudinger-Moser nonlinearities [PDF]
arXiv, 2020 We establish some existence results for a class of critical elliptic problems with singular exponential nonlinearities. We do not assume any global sign conditions on the nonlinearity, which makes our results new even in the nonsingular case.
arxiv