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pro vyhledávání: '"35j10"'
Autor:
Xu, Ziyi
We investigate the $W^{1,p}$ estimates of the Neumann problem for the Schr\"odinger equation $-\Delta u+ V u={\rm div}(f)$ in the region above a convex graph. For any $p>2$, we obtain a sufficient condition for the $W^{1,p}$ solvability. As a result,
Externí odkaz:
http://arxiv.org/abs/2411.18852
In this paper we investigate the $L^p$ regularity, $L^p$ Neumann and $W^{1,p}$ problems for generalized Schr\"odinger operator $-\text{div}(A\nabla )+ V $ in the region above a Lipschitz graph under the assumption that $A$ is elliptic, symmetric and
Externí odkaz:
http://arxiv.org/abs/2411.18458
Autor:
Dumont, Arnaud, Morris, Andrew J.
We obtain Riesz transform bounds and characterise operator-adapted Hardy spaces to solve boundary value problems for singular Schr\"odinger equations $-\mathrm{div}(A\nabla u)+aVu=0$ in the upper half-space $\mathbb{R}^{1+n}_{+}$ with boundary dimens
Externí odkaz:
http://arxiv.org/abs/2411.17563
Autor:
Dewan, Utsav
In this article, we consider the Schr\"odinger equation corresponding to the Laplace-Beltrami operator with radial initial data on Damek-Ricci spaces and study the Carleson's problem of pointwise convergence of the solution to its initial data along
Externí odkaz:
http://arxiv.org/abs/2411.14020
Energy-based fragmentation methods approximate the potential energy of a molecular system as a sum of contribution terms built from the energies of particular subsystems. Some such methods reduce to truncations of the many-body expansion (MBE); other
Externí odkaz:
http://arxiv.org/abs/2411.12467
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
Autor:
Chen, Cong, Wang, Hua
Let us consider the Schr\"{o}dinger operator $\mathcal{L}=-\Delta+V$ on $\mathbb R^d$ with $d\geq3$, where $\Delta$ is the Laplacian operator on $\mathbb R^d$ and the nonnegative potential $V$ belongs to certain reverse H\"{o}lder class $RH_s$ with $
Externí odkaz:
http://arxiv.org/abs/2411.04377
Autor:
Dewan, Utsav, Ray, Swagato K.
Let $\Delta$ be the Laplace-Beltrami operator on a Damek-Ricci space $S$ corresponding to the left-invariant Riemannian metric, with its $L^2$-spectrum being the half line $(-\infty, -Q^2/4]$. Then for a radial $L^2$-Schwartz class function $f$, we c
Externí odkaz:
http://arxiv.org/abs/2411.04084
Autor:
Chorfi, S. E.
In this paper, we prove a sharp uniqueness result for the singular Schr\"odinger equation with an inverse square potential. This will be done without assuming geometrical restrictions on the observation region. The proof relies on a recent technique
Externí odkaz:
http://arxiv.org/abs/2410.21466
In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\"odinger equation with dynamic boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the inverse s
Externí odkaz:
http://arxiv.org/abs/2410.21123