Regularity results on a class of doubly nonlocal problems
TLDR
In this article, an issue of regularity of weak solution to the problem (see below) is addressed and the question of H s versus C 0 -weighted minimizers of the functional associated to problem (P) is investigated.About:
This article is published in Journal of Differential Equations.The article was published on 2020-04-15 and is currently open access. It has received 16 citations till now. The article focuses on the topics: Weak solution & Class (set theory).read more
Citations
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Journal ArticleDOI
Singular Doubly Nonlocal Elliptic Problems with Choquard Type Critical Growth Nonlinearities
TL;DR: In this article, a very singular and doubly nonlocal singular problem with singular nonlinearity was studied and a very weak comparison principle and the optimal Sobolev regularity was established.
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Multiplicity and concentration results for fractional Choquard equations: Doubly critical case
TL;DR: In this paper, a generalization of the refined Sobolev inequality with Morrey norm is presented, and the multiplicity and concentration results are obtained in the case where F ( u ) has the lower critical exponent 2 α ♯, which remains unsolved in the existing literature.
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Existence and nonexistence results for Kohn Laplacian with Hardy-Littlewood-Sobolev critical exponents
Divya Goel,Konijeti Sreenadh +1 more
TL;DR: In this paper, the authors studied the Dirichlet problem with Choquard type non linearity and derived the Brezis-Nirenberg type result for the problem.
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Interior and boundary regularity results for strongly nonhomogeneous p,q-fractional problems
TL;DR: In this article, the global regularity of weak solutions to a class of problems involving the fractional (p,q) Laplacian, denoted by $(-\Delta)^{s_1}_{p}+(-\Delta )^{ s_2}_{q}), is investigated.
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Multiple positive solutions for degenerate Kirchhoff equations with singular and Choquard nonlinearity
Sushmita Rawat,Konijeti Sreenadh +1 more
TL;DR: In this article, the existence, multiplicity and regularity of positive weak solutions for the following Kirchhoff-Choquard problem were studied, and it was shown that each positive weak solution is bounded and satisfy Holder regularity.
References
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Book
Singular Integrals and Differentiability Properties of Functions.
TL;DR: Stein's seminal work Real Analysis as mentioned in this paper is considered the most influential mathematics text in the last thirty-five years and has been widely used as a reference for many applications in the field of analysis.
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Functional Analysis, Sobolev Spaces and Partial Differential Equations
TL;DR: In this article, the theory of conjugate convex functions is introduced, and the Hahn-Banach Theorem and the closed graph theorem are discussed, as well as the variations of boundary value problems in one dimension.
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Hitchhiker's guide to the fractional Sobolev spaces
TL;DR: In this article, the authors deal with the fractional Sobolev spaces W s;p and analyze the relations among some of their possible denitions and their role in the trace theory.
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Regularity of the obstacle problem for a fractional power of the laplace operator
TL;DR: In this article, the authors studied the problem of finding the optimal regularity result for the contact set of a function ϕ and s ∈ (0, 1) when ϕ is C 1,s or smoother, and showed that the solution u is in the space c 1,α for every α < s.
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Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
TL;DR: In this article, the Hartree-Fock theory of a plasma was used to prove existence and uniqueness of a minimization of the functional function of an electron trapped in its own hole.