Fractional variational problems with the Riesz-Caputo derivative [PDF]
, 2012 In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the ...
Almeida, R. +2 more
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Riesz potentials of functions in L^{p} [PDF]
, 2006 Bu tez beş bölümden oluşmaktad¬ Birinci bölümde çal¬ mam¬ için gereklis s r. şs zolan tan¬ ve temel teoremler, ikinci bölümde Fourier Dönüşümleri, Rieszm sPotansiyeli, Fourier Dönüşümü ile Riesz Potansiyeli aras¬s ndaki ilişkiler ve Rieszsgrup ...
Dal, İlyas
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A trace inequality for generalized potentials in Lebesgue spaces with variable exponent
Journal of Function Spaces and Applications, 2004 A trace inequality for the generalized Riesz potentials Iα(x) is established in spaces Lp(x) defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces.
David E. Edmunds +2 more
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An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces
Advances in Nonlinear Analysis, 2020 It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
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Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms
Journal of Function Spaces, 2019 Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz ...
Hua Wang
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Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results
Photonics, 2021 The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schrödinger equation (NLSE) including fractional one-dimensional or two-dimensional diffraction
Boris A. Malomed
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The role of Riesz potentials in the weak-strong uniqueness for Euler-Poisson systems [PDF]
, 2023 In this article, the weak-strong uniqueness principle is proved for an Euler-Poisson system in the whole space, with initial data so that the strong solution exists.
Alves, Nuno J.
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Globally Existing Solutions to the Problem of Dirichlet for the Fractional 3D Poisson Equation
Fractal and Fractional, 2023 A general approach to solving the Dirichlet problem, both for bounded 3D domains and for their unbounded complements, in terms of the fractional (3D) Poisson equation, is presented.
Toshko Boev, Georgi Georgiev
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Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces [PDF]
, 2014 summary:Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces.
Ohno, Takao, Shimomura, Tetsu
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On the (p,q)-Boundedness of Nonisotropic Spherical Riesz Potentials
Journal of Inequalities and Applications, 2007 We introduced the concept of nonisotropic spherical Riesz potential operators generated by the λ-distance of variable order on λ-sphere and its (p,q)-boundedness were investigated.
Mehmet Zeki Sarikaya +1 more
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