The Scott conjecture for large Coulomb systems: a review
We review some older and more recent results concerning the energy and particle
distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic …
distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic …
[图书][B] Singularities of solutions to chemotaxis systems
P Biler - 2019 - books.google.com
The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing
concentration phenomena in physics and biology. While the two-dimensional theory is by …
concentration phenomena in physics and biology. While the two-dimensional theory is by …
[HTML][HTML] Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings
In this paper we discuss non-local operators with killing potentials, which may not be in the
standard Kato class. We first discuss factorization of their Dirichlet heat kernels in metric …
standard Kato class. We first discuss factorization of their Dirichlet heat kernels in metric …
Equivalence of Sobolev norms involving generalized Hardy operators
We consider the fractional Schrödinger operator with Hardy potential and critical or
subcritical coupling constant. This operator generates a natural scale of homogeneous …
subcritical coupling constant. This operator generates a natural scale of homogeneous …
Fractional Hardy-Sobolev equations with nonhomogeneous terms
This paper deals with existence and multiplicity of positive solutions to the following class of
nonlocal equations with critical nonlinearity:(− Δ) su− γ u| x| 2 s= K (x)| u| 2 s∗(t)− 2 u| x| t+ f …
nonlocal equations with critical nonlinearity:(− Δ) su− γ u| x| 2 s= K (x)| u| 2 s∗(t)− 2 u| x| t+ f …
Self-similarity in homogeneous stationary and evolution problems
JW Cholewa, A Rodriguez-Bernal - Journal of Evolution Equations, 2023 - Springer
We analyse self-similarity properties related to linear elliptic and evolutionary problems
involving homogeneous operators in several spaces including measures. We employ these …
involving homogeneous operators in several spaces including measures. We employ these …
Heat kernel estimates of fractional Schrödinger operators with negative Hardy potential
T Jakubowski, J Wang - Potential Analysis, 2020 - Springer
We obtain two-sided estimates for the heat kernel (or the fundamental function) associated
with the following fractional Schrödinger operator with negative Hardy potential Δ α/2− λ| x …
with the following fractional Schrödinger operator with negative Hardy potential Δ α/2− λ| x …
Generalized Hardy operators
P D'Ancona - Nonlinearity, 2023 - iris.uniroma1.it
Consider the operator on $ L^{2}(\mathbb {R}^ d) $\begin {equation*}%\label {defn-La}\La=(-
\Delta)^{\alpha/2}+ a| x|^{-\alpha}\quad\text {with}\quad 0<\alpha<\min\{2, d\}.\end …
\Delta)^{\alpha/2}+ a| x|^{-\alpha}\quad\text {with}\quad 0<\alpha<\min\{2, d\}.\end …
Optimal Hardy inequality for the fractional Laplacian on Lp
K Bogdan, T Jakubowski, J Lenczewska… - Journal of Functional …, 2022 - Elsevier
Optimal Hardy inequality for the fractional Laplacian on Lp - ScienceDirect Skip to main
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Hardy perturbations of subordinated Bessel heat kernels
arXiv:2409.02853v1 [math.AP] 4 Sep 2024 Page 1 arXiv:2409.02853v1 [math.AP] 4 Sep 2024
HARDY PERTURBATIONS OF SUBORDINATED BESSEL HEAT KERNELS KRZYSZTOF …
HARDY PERTURBATIONS OF SUBORDINATED BESSEL HEAT KERNELS KRZYSZTOF …