相关论文: Interior Lp-estimates for elliptic and parabolic S…

We obtain $L_p$ estimates for fractional parabolic equations with space-time non-local operators $$ \partial_t^\alpha u - Lu + \lambda u= f \quad \mathrm{in} \quad (0,T) \times \mathbb{R}^d,$$ where $\partial_t^\alpha u$ is the Caputo…

We consider a divergence form hypoelliptic operator consisting of a system of real smooth vector fields $X_{1},..., X_{q}$ satisfying H\"ormander condition in some domain $\Omega\subseteq\erren$. Interior $L^{p}$ estimates, $2\leq…

We obtain sharp parabolic interior and global Schauder estimates for solutions to nonlocal space-time master equations $(\partial_t +L)^su = f$ in $\mathbb{R} \times \Omega$, where $L$ is an elliptic operator in divergence form, subject to…

We study nonlocal elliptic and parabolic equations on $C^{1,\tau}$ open sets in weighted Sobolev spaces, where $\tau\in (0,1)$. The operators we consider are infinitesimal generators of symmetric stable L\'evy processes, whose L\'evy…

We study the $L^p$-theory for the Schr\"odinger operator $\mathcal L_a$ with inverse-square potential $a|x|^{-2}$. Our main result describes when $L^p$-based Sobolev spaces defined in terms of the operator $(\mathcal L_a)^{s/2}$ agree with…

We prove resolvent estimates in the Euclidean setting for Schr\"{o}dinger operators with potentials in Lebesgue spaces: $-\Delta+V$. The $(L^{2}, L^{p})$ estimates were already obtained by Blair-Sire-Sogge, but we extend their result to…

We study eigenvalues of non-self-adjoint Schr\"odinger operators on non-trapping asymptotically conic manifolds of dimension $n\ge 3$. Specifically, we are concerned with the following two types of estimates. The first one deals with Keller…

In this article, the authors consider the Schr\"{o}dinger type operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix $A$ satisfies uniformly elliptic condition and the nonnegative potential $V$ belongs to…

In the first part of the paper the authors study the minimal and maximal extension of a class of weighted pseudodifferential operators in the Fr\'echet space $L^p_{\rm loc}(\Omega)$. In the second one non homogeneous microlocal properties…

In this article, we investigate the unweighted and weighted $L^p$-boundedness of pseudo-multipliers associated with a class of Schr\"odinger operators. The weight classes we consider are tailored to this framework and strictly contain the…

We develop local elliptic regularity for operators having coefficients in a range of Sobolev-type function spaces (Bessel potential, Sobolev-Slobodeckij, Triebel-Lizorkin, Besov) where the coefficients have a regularity structure typical of…

In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schr\"odinger operator $\mathcal{L}=-\Delta+V$ in $\mathbb{R}^d$, where $d>2$ and the…

The aim of this work is to study the continuity and compactness of the operators $W^{1, q}(\Omega ; \mathtt {V}_0, \mathtt {V}_1 ) \rightarrow L^{q_0} (\Omega ; \mathtt {V}_2)$ and $W^{1, q} (\Omega ; \mathtt {V}_0, \mathtt {V}_1 )…

We show various $L^p$ estimates for Schr\"odinger operators $-\Delta+V$ on $\RR^n$ and their square roots. We assume reverse H\"older estimates on the potential, and improve some results of Shen \cite{Sh1}. Our main tools are improved…

We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order…

Let $L:=-\Delta+V$ be the Schr\"{o}dinger operator on $\mathbb{R}^n$ with $n\geq 3$, where $V$ is a non-negative potential which belongs to certain reverse H\"{o}lder class $RH_q(\mathbb{R}^n)$ with $q\in (n/2,\,\infty)$. In this article,…

The paper deals with the operator $u\rightarrow gu$ defined in the Sobolev space $W^{r,p}(\Omega)$ and which takes values in $L^p(\Omega)$ when $\Omega$ is an unbounded open subset in $R^n$. The functions $g$ belong to wider spaces of $L^p$…

Let $H_V=-\Delta +V$ be a Schr\"odinger operator on an arbitrary open set $\Omega$ of $\mathbb R^d$, where $d \geq 3$, and $\Delta$ is the Dirichlet Laplacian and the potential $V$ belongs to the Kato class on $\Omega$. The purpose of this…

Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with $\sigma\geq n/2$. The aim of this paper is to study the $A_p$ weights associated to $L$,…

We establish the maximal regularity for nonautonomous Ornstein-Uhlenbeck operators in $L^p$-spaces with respect to a family of invariant measures, where $p\in (1,+\infty)$. This result follows from the maximal $L^p$-regularity for a class…