Zobrazeno 1 - 10
of 68 497
pro vyhledávání: '"P. A. Sobolev"'
Autor:
Yang, Minbo, Zhao, Shunneng
In this paper, we consider the following nonlocal Soblev-type inequality \begin{equation*} C_{HLS}\big(\int_{\mathbb{R}^n}\big(|x|^{-\mu} \ast u^{p}\big)u^{p} dx\big)^{\frac{1}{p}}\leq\int_{\mathbb{R}^n}|\nabla u|^2 dx , \quad \forall~u\in D^{1,2}(\m
Externí odkaz:
http://arxiv.org/abs/2501.01927
For any integer $ p \geq 2 $, we construct a compact Riemannian manifold $ \mathcal{N} $, such that if $ \dim \mathcal{M} > p $, there is a map in the Sobolev space of mappings $ W^{1,p} (\mathcal{M}, \mathcal{N})$ which is not a weak limit of smooth
Externí odkaz:
http://arxiv.org/abs/2412.12889
Autor:
Van Schaftingen, Jean
We prove that a mapping $u \colon \mathcal{M}'\to \mathcal{N}$, where $\mathcal{M}'$ and $ \mathcal{N}$ are compact Riemannian manifolds, is the trace of a Sobolev mapping $U \colon \mathcal{M}' \times [0, 1) \to \mathcal{N}$ if and only if it is on
Externí odkaz:
http://arxiv.org/abs/2412.12713
This paper revisits classical fractional Sobolev embedding theorems and the algebra property of the fractional Sobolev space $H^s(\mathbb{R})$ by means of Haar functions and dyadic decompositions. The aim is to provide an alternative, hands-on approa
Externí odkaz:
http://arxiv.org/abs/2412.12051
Autor:
Nidhi, Sreenadh, K.
In this paper we study the existence and regularity results of normalized solutions to the following quasilinear elliptic Choquard equation with critical Sobolev exponent and mixed diffusion type operators: \begin{equation*} \begin{array}{rcl} -\Delt
Externí odkaz:
http://arxiv.org/abs/2412.11469
The Stein Variational Gradient Descent method is a variational inference method in statistics that has recently received a lot of attention. The method provides a deterministic approximation of the target distribution, by introducing a nonlocal inter
Externí odkaz:
http://arxiv.org/abs/2412.10295
In this paper, we consider a fractional p-Laplacian system of equations in the entire space RN with doubly critical singular nonlinearities involving a local critical Sobolev term together with a nonlocal Choquard critical term; the problem also incl
Externí odkaz:
http://arxiv.org/abs/2412.09650
Autor:
Dietze, Charlotte, Nam, Phan Thành
We give a new proof of the compactness of minimizing sequences of the Sobolev inequalities in the critical case. Our approach relies on a simplified version of the concentration-compactness principle, which does not require any refinement of the Sobo
Externí odkaz:
http://arxiv.org/abs/2412.08616
We consider the boundedness and exponential integrability of solutions to the Dirichlet problem for the degenerate elliptic equation % \[ -v^{-1}\mathrm{Div}(|\sqrt{Q}\nabla u|^{p-2}Q\nabla u)=f|f|^{p-2}, \quad 1
Externí odkaz:
http://arxiv.org/abs/2412.07540
An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds
Autor:
Nobili, Francesco
We review recent results regarding the problem of the stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds. We shall describe techniques and methods from smooth and non-smooth geometry, the fruitful combination
Externí odkaz:
http://arxiv.org/abs/2412.05935