9 citations · 16 across the 16 of their papers we have counts for
17 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…
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…
Existence of solutions to a quasilinear nonlocal PDE
Lisbeth Carrero, Alexander Quaas, Andres Zuniga
In this paper, we introduce a new class of quasilinear operators, which represents a nonlocal version of the operator studied by Stuart and Zhou [1], inspired by models in nonlinea…
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…
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,…
The limit as of the fractional convex envelope
Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas +1
We study the behavior of the fractional convexity when the fractional parameter goes to 1. For any notion of convexity, the convex envelope of a datum prescribed on the boundary of…
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…
Fundamental solutions and critical Lane-Emden exponents for nonlinear integral operators in cones
Gabrielle Nornberg, Disson dos Prazeres, Alexander Quaas
In this article we study the fundamental solutions or "-harmonic functions" for some nonlinear positive homogeneous nonlocal elliptic problems in conical domains, such as \begin…
Large harmonic functions for fully nonlinear fractional operators
Gonzalo Dávila, Alexander Quaas, Erwin Topp
We study existence, uniqueness and boundary blow-up profile for fractional harmonic functions on a bounded smooth domain . We deal with harmonic functions ass…
The evolution problem associated with the fractional first eigenvalue
Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas +1
In this paper we study the evolution problem associated with the first fractional eigenvalue. We prove that the Dirichlet problem with homogeneous boundary condition is well posed…
The sharp exponent in the study of the nonlocal Hénon equation in . A Liouville theorem and an existence result
B. Barrios, A. Quaas
We will consider the nonlocal Hénon equation where is the fractional Laplacian operator with , , and $N…
Periodic solutions for the one-dimensional fractional Laplacian
B. Barrios, J. García-Melián, A. Quaas
In this paper we are concerned with the construction of periodic solutions of the nonlocal problem in , where stands for the -Laplacian, $s…
A Liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions
B. Barrios, L. Del Pezzo, J. Garcia-Melian +1
In this work we obtain a Liouville theorem for positive, bounded solutions of the equation where stands for the f…
Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
B. Barrios, L. Del Pezzo, J. Garcia-Melian +1
In this paper we consider classical solutions of the semilinear fractional problem in with in ,…
A priori bounds and existence of solutions for some nonlocal elliptic problems
B. Barrios, L. Del Pezzo, J. García-Melián +1
In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degre…
Solvability of nonlinear elliptic equations with gradient terms
Patricio Felmer, Alexander Quaas, Boyan Sirakov
We study the solvability in the whole Euclidean space of coercive quasi-linear and fully nonlinear elliptic equations modeled on , , where and…