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Some nonlocal optimal design problems
(Academic Press Inc Elsevier Science, 2018-03)
In this paper we study two optimal design problems associated to fractional Sobolev spaces Ws,p(Ω). Then we find a relationship between these two problems and finally we investigate the convergence when s↑1.
Scalar field equation with non-local diffusion
(Springer, 2015)
In this paper we are interested on the existence of ground state solutions for fractional field equations of the form
integral (I - Delta)(alpha) u = f(x, u) in IRN, u > 0 in IRN, lim(vertical bar x vertical bar ...
Mixed methods for degenerate elliptic problems and application to fractional Laplacian
(EDP Sciences, 2021-02-26)
We analyze the approximation by mixed finite element methods of solutions of equations of the form −div (a∇u) = g, where the coefficient a = a(x) can degenerate going to zero or infinity. First, we extend the classic error ...
Finite element approximations for fractional evolution problems
(De Gruyter, 2019-07-30)
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we ...
H-convergence result for nonlocal elliptic-type problems via tartar's method
(Society for Industrial and Applied Mathematics, 2017-07)
In this work we obtain a compactness result for the H-convergence of a family of nonlocal and nonlinear monotone elliptic-type problems by means of Tartar's method of oscillating test functions.
Study of the Existence of Supersolutions for Nonlocal Equations with Gradient Terms
(Birkhauser Verlag Ag, 2020-07)
We study the existence of positive supersolutions of nonlocal equationsof type (- Δ) su+ | Δ u| q= λf(u) posed in exterior domains where the datum f canbe comparable with up near the origin. We prove that the existence of ...
Some results on a pseudo-relativistic Hartree equation and on a magnetic Choquard equation
(Universidade Federal de Minas GeraisBrasilICEX - INSTITUTO DE CIÊNCIAS EXATASPrograma de Pós-Graduação em MatemáticaUFMG, 2020-11-03)
A Capacity-Based Condition for Existence of Solutions to Fractional Elliptic Equations with First-Order Terms and Measures
(Springer, 2020-09)
In this manuscript, we appeal to Potential Theory to provide a sufficient condition for existence of distributional solutions to fractional elliptic problems with non-linear first-order terms and measure data ω:{(−Δ)su=| ...
Infinitely Many Solutions For A Critical Kirchhoff Type Problem Involving A Fractional Operator
(KHAYYAM PUBL CO INCATHENS, 2016)
A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian
(2016)
We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Delta)(alpha)u = v(q) in R-N, (-Delta)(alpha)v = u(p) in R-N, where alpha is an element of (0, 1), N > 2 alpha and p, q are positive real numbers ...