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pro vyhledávání: '"35a08"'
In this paper, we deal with the following mixed local/nonlocal Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{ll} - \Delta u + (-\Delta)^s u+u = u^p \quad \hbox{in $\mathbb{R}^n$,} u>0 \quad \hbox{in $\mathbb{R}^n$,} \lim\limits_{|x
Externí odkaz:
http://arxiv.org/abs/2411.09941
The aim of this paper is to study a Laplace-type operator and its fundamental solution on the characteristic plane in the Heisenberg group $\mathbb{H}^2$. We introduce a conformal version of the Laplacian and we prove that the distance induced by the
Externí odkaz:
http://arxiv.org/abs/2410.23256
Autor:
Schaback, Robert
This paper constructs unique compactly supported functions in Sobolev spaces that have minimal norm, maximal support, and maximal central value, under certain renormalizations. They may serve as optimized basis functions in interpolation or approxima
Externí odkaz:
http://arxiv.org/abs/2409.01759
Autor:
Strunz, Pavel
Orthogonal coordinate systems enable expressing the boundary conditions of differential equations in accord with the physical boundaries of the problem. It can significantly simplify calculations. The orthogonal similar oblate spheroidal (SOS) coordi
Externí odkaz:
http://arxiv.org/abs/2405.17063
Autor:
Biagi, Stefano, Bramanti, Marco
We consider Kolmogorov-Fokker-Planck operators of the form $$ \mathcal{L}u=\sum_{i,j=1}^{q}a_{ij}(x,t)u_{x_{i}x_{j}}+\sum_{k,j=1}^{N} b_{jk}x_{k}u_{x_{j}}-\partial_{t}u, $$ with $\left( x,t\right) \in\mathbb{R}^{N+1},N\geq q\geq1$. We assume that $a_
Externí odkaz:
http://arxiv.org/abs/2405.09358
We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally H\"older continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and uniqueness
Externí odkaz:
http://arxiv.org/abs/2405.01955
Autor:
Galeotti, Mattia
In their celebrated paper of 1976, Rothschild and Stein prove a lifting procedure that locally reduces to a free nilpotent Lie algebra any family of smooth vector fields $X_1,\dots,X_q$, over a manifold $M$. Then, a large class of differential operat
Externí odkaz:
http://arxiv.org/abs/2403.19619
The fractional diffraction optics theory has been elaborated using the Green function technique. The optics-fractional equation describing the diffraction X-ray scattering by imperfect crystals has been derived as the fractional matrix integral Fredh
Externí odkaz:
http://arxiv.org/abs/2404.11618
Autor:
Eiter, Thomas, Silvestre, Ana Leonor
This paper is concerned with integral representations and asymptotic expansions of solutions to the time-periodic incompressible Navier-Stokes equations for fluid flow in the exterior of a rigid body that moves with constant velocity. Using the time-
Externí odkaz:
http://arxiv.org/abs/2402.12213
Publikováno v:
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021
The paper is devoted to understand the large time behaviour and decay of the solution of the discrete heat equation in the one dimensional mesh $\Z$ on $\ell^p$ spaces, and its analogies with the continuous-space case. We do a deep study of the momen
Externí odkaz:
http://arxiv.org/abs/2401.16377