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The Semigroup and the Inverse of the Laplacian on the Heisenberg Group
(Universidad de La Frontera. Departamento de Matemática y EstadísticaUniversidade Federal de Pernambuco. Departamento de Matemática, 2010)
On the fractional Laplacian and nonlocal operators
(2018)
The aim of this work is to study certain type of operators that have adquired a renewed relevance in the last decade. This wide class of operators, genericaly called nonlocal operators, appears naturally in many applications ...
Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term
(2020-02-01)
In this work we study a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term. The problem requires the definition of a suitable sense of solution, which allows us to show the existence of a ...
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator
(2021-08-01)
In this work we study a quasilinear elliptic problem involving the 1-Laplacian operator in RN, whose nonlinearity satisfy conditions similar to those ones of the classical work of Berestycki and Lions. Several difficulties ...
Multiple Ordered Solutions for a Class of Problems Involving the 1-Laplacian Operator
(2022-04-01)
In this paper, we use minimax methods, comparison arguments, and an approximation result to show the existence and multiplicity of solutions for the following class of problems: {-Δ1v=λf(v)inΩ,v≥0inΩ,v=0on∂Ω,where Ω is a ...
Nodal Solutions to Quasilinear Elliptic Problems Involving the 1-Laplacian Operator via Variational and Approximation Methods
(Indiana Univ Math Journal, 2022-01-01)
In this work we use two different methods to get nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator. In the first one, we develop an approach based on a minimization of the energy functional ...
Laplacian coordinates: Theory and methods for seeded image segmentation
(2021-08-01)
Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated ...
Strauss’ and Lions’ Type Results in BV(RN) with an Application to an 1-Laplacian Problem
(2018-06-01)
In this work we state and prove versions of some classical results, in the framework of functionals defined in the space of functions of bounded variation in RN. More precisely, we present versions of the Radial Lemma of ...
Existence and Profile of Ground-State Solutions to a 1-Laplacian Problem in RN
(2020-09-01)
In this work we prove the existence of ground state solutions for the following class of problems {-Δ1u+(1+λV(x))u|u|=f(u),x∈RN,u∈BV(RN),where λ> 0 , Δ 1 denotes the 1-Laplacian operator which is formally defined by ...
Anisotropic 1-Laplacian problems with unbounded weights
(2021-12-01)
In this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One ...