Zobrazeno 1 - 10
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pro vyhledávání: '"35a15"'
We study a system of drift-diffusion PDEs for a potentially infinite number of incompressible phases, subject to a joint pointwise volume constraint. Our analysis is based on the interpretation as a collection of coupled Wasserstein gradient flows or
Externí odkaz:
http://arxiv.org/abs/2411.13969
We study a Dirichlet problem driven by the (degenerate or singular) fractional $p$-Laplacian and involving a $(p-1)$-superlinear reaction at infinity, not necessarily satisfying the Ambrosetti-Rabinowitz condition. Using critical point theory, trunca
Externí odkaz:
http://arxiv.org/abs/2411.10119
In this paper, we study a coupled Hartree-type system given by \[ \left\{ \begin{array}{ll} -\Delta u = K_{1}(x)(|x|^{-(N-\alpha)} * K_{1}(x)v^{2^{*}_{\alpha}})v^{2^{*}_{\alpha}-1} & \text{in } \mathbb{R}^N, \\[1mm] -\Delta v = K_{2}(x)(|x|^{-(N-\alp
Externí odkaz:
http://arxiv.org/abs/2411.09993
Autor:
Musina, Roberta, Nazarov, Alexander I.
We continue our investigation of Hardy-type inequalities involving combinations of cylindrical and spherical weights. Compared to [Cora-Musina-Nazarov, Ann. Sc. Norm. Sup., 2024], where the quasi-spherical case was considered, we handle the full rang
Externí odkaz:
http://arxiv.org/abs/2411.08585
Autor:
Cohen, David W.
A new adaptation of the Wasserstein metric over the space of probability measures is presented, the associated formal Otto calculus developed, and some transport inequalities are proven. An instance of this new metric can be viewed as a curved versio
Externí odkaz:
http://arxiv.org/abs/2411.05696
We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: $$ (-\Delta)^s u+V(\epsilon x)u=\lambda u+\left(I_\alpha *|u|^q\right)|u|^{q-2} u+\left(I_\alpha *|u|^p\right)|u|^{p-2} u, \quad x \in \mat
Externí odkaz:
http://arxiv.org/abs/2411.01476
This paper deals with Gelfand-type problems \begin{equation}\label{Gelfand10} \qquad\qquad\left\{\begin{array}{ll} - \Delta_m u = \lambda f(u), \quad&\hbox{in} \ \Omega, \ \lambda >0, \\[10pt] u =0, \quad&\hbox{on} \ \partial_m\Omega, \end{array} \ri
Externí odkaz:
http://arxiv.org/abs/2410.21927
Autor:
Prasad, Harsh, Tewary, Vivek
We prove existence, uniqueness and initial time regularity for variational solutions to nonlocal total variation flows associated with image denoising and deblurring. In particular, we prove existence of parabolic minimisers $u$, that is, $$\int_0^T\
Externí odkaz:
http://arxiv.org/abs/2410.17649
In this paper, we study the existence of normalized solutions for the following $(2, q)$-Laplacian equation \begin{equation*}\label{Eq-Equation1} \left\{\begin{array}{l} -\Delta u-\Delta_q u+\lambda u=f(u) \quad x \in \mathbb{R}^N , \\ \int_{\mathbb{
Externí odkaz:
http://arxiv.org/abs/2410.15066
We show an abstract critical point theorem about existence of infinitely many critical orbits to strongly indefinite functionals with sign-changing nonlinear part defined on a dislocation space with a discrete group action. We apply the abstract resu
Externí odkaz:
http://arxiv.org/abs/2410.13315