Results 71 to 80 of about 644 (181)

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons

Communications on Pure and Applied Mathematics, Volume 79, Issue 5, Page 1151-1298, May 2026.
Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
wiley   +1 more source

Evans potentials and the Riesz decomposition

Hiroshima Mathematical Journal, 2008
This paper is concerned with Riesz-type decomposition for superharmonic functions in parabolic manifolds. The main result of the paper provides a necessary and sufficient condition for such a decomposition in terms of the spherical mean induced by the Evans kernels.
openaire   +2 more sources

Vector Solutions for Linearly Coupled Choquard Type Equations with Lower Critical Exponents

Advances in Mathematical Physics, 2020
The existence, nonexistence, and multiplicity of vector solutions of the linearly coupled Choquard type equations −Δu+V1xu=Iα∗uN+α/Nuα/N−1u+λv,x∈ℝN,−Δv+V2xv=Iα∗vN+α/Nvα/N−1v+λu,x∈ℝN,u,v∈H1ℝN, are proved, where α∈0,N, N≥3, V1xV2x∈L∞ℝN are positive ...
Huiling Wu
doaj   +1 more source

On the differentiability of Riesz potentials of functions

Hiroshima Mathematical Journal, 1987
The Riesz potential of order \(\alpha\) of a nonnegative measurable function f on \(R^ n\) is defined by \(R_{\alpha}f(x)=\int R_{\alpha}(x-y)f(y)dy,\) where \(R_{\alpha}(x)=| x|^{\alpha - n}\) if \(\alpha 1\) and f be a nonnegative measurable function on \(R^ n\) such that \(R_ mf\not\equiv \infty\) and \[ \int f(y)^ p(\log (2+f(y))^{\delta} dyp-1. \]
openaire   +3 more sources

A Physical Interpretation of Riesz Potential

IOSR Journal of Mathematics, 2016
In this paper we add a physical meaning to the Riesz potential by using Newtonian force fields due to a body and velocity fields of any fluid. To do this, we firstly give some properties of Newtonian force fields and correspondingly Newtonian potentials.
Esin İnan Eskitaşçioğlu, Mehmet Açil   +1 more
openaire   +1 more source

Estimates for capacities and traces of potentials

International Journal of Mathematics and Mathematical Sciences, 1984
It is shown that “isoperimetric” inequalities, relating measures and capacities, hold for all sets in ℝn if they are valid for all balls. As a corollary, the necessary and sufficient conditions for the continuity of some imbeddings of M. Riesz and Bessel
V. G. Maz'ja, S. P. Preobrazenskii
doaj   +1 more source

Regularity for the second order Riesz transforms associated with Schrödinger operators on weighted BMO type spaces

ITM Web of Conferences, 2018
Let L = −Δ + V be a Schrödinger operator on ℝn, where V is a nonnegative potential satisfying the suitable reverse Hölder’s inequality. In this paper, we study the boundedness of the second order Riesz transforms such as L−1∇2 on the spaces of BMO type ...
Nguyen Ngoc Trong, Nguyen Anh Dao, Truong L. X.   +2 more
doaj   +1 more source

Characterization of balls by Riesz-potentials

Annali di Matematica Pura ed Applicata, 2008
This paper presents a nice characterization of balls in \(\mathbb R^N\), \(N\geq 2\), in terms of generalized Riesz potentials. More precisely, let \(\Omega\subset\mathbb R^N\) be a bounded convex domain and \(u(x)=\int_\Omega |x-y|^{\alpha-N}dy ...
openaire   +2 more sources

Weighted Hardy and Potential Operators in Morrey Spaces

Journal of Function Spaces and Applications, 2012
We study the weighted p→q-boundedness of Hardy-type operators in Morrey spaces ℒp,λ(ℝn) (or ℒp,λ(ℝ+1) in the one-dimensional case) for a class of almost monotonic weights.
Natasha Samko
doaj   +1 more source

Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian

Advances in Mathematical Physics
In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N≥3, F represents the primitive function of f,  f∈CR;R is a function that fulfils the general ...
Sarah Abdullah Qadha, Muneera Abdullah Qadha, Haibo Chen, Yuying Zao   +3 more
doaj   +1 more source