7 papers
Ergodic pairs for fractional Hamilton-Jacobi equations on bounded domains: large solutions
Alexander Quaas, Erwin Topp
In this article, we study the ergodic problem associated to viscous Hamilton-Jacobi equation where the diffusion is governed by the censored fractional Laplacian, a nonlocal ellipt…
Nonexistence of positive supersolutions for semilinear fractional elliptic equations in exterior domains
Reshmi Biswas, Alexander Quaas
This article is concerned with the nonexistence of positive solutions for nonlinear fractional elliptic inequalities in exterior domains of , . We would like t…
Propagation in the Fisher-KPP equation with Mixed Operator
Begoña Barrios, Bryan Pichucho, Alexander Quaas
Our investigation focuses on the asymptotic spreading behavior of the Fisher-KPP equation with a mixed local-nonlocal operator in the diffusion (see the work by X. Cabré and J.-M.…
Mixed local and nonlocal laplacian without standard critical exponent for Lane-Emden equation
Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas
In this paper, we investigate a mixed elliptic equation involving both local and nonlocal Laplacian operators, with a power-type nonlinearity. Specifically, we consider a Lane-Emde…
The fundamental solution of the fractional p-laplacian
Leandro M. Del Pezzo, Alexander Quaas
In this article, we find the fundamental solution of the fractional p-laplacian and use them to prove two different Liouville-type theorems. A non-existence classical Liouville-typ…
Nonlocal Liouville theorems with gradient nonlinearity
Anup Biswas, Alexander Quaas, Erwin Topp
In this article we consider a large family of nonlinear nonlocal equations involving gradient nonlinearity and provide a unified approach, based on the Ishii-Lions type technique,…