相关论文: Strong unique continuation for the higher order fr…

We extend the potential theory on almost minimzers from Part 1. We introduce so-called Hardy structures to study many classical operators using the tools from part 1. Furthermore, we show that for a naturally defined operator L, minimal…

In this paper, we develop a numerical multiscale method to solve the fractional Laplacian with a heterogeneous diffusion coefficient. When the coefficient is heterogeneous, this adds to the computational costs. Moreover, the fractional…

In this paper, we study the effect of Hardy potential on the existence or non-existence of solutions to a fractional Laplacian problem involving a singular nonlinearity. Also, we mention a stability result.

In this work, we establish results on the continuity of strongly singular Calder\'on-Zygmund operators of type $\sigma$ on Hardy spaces $H^p(\mathbb{R}^n)$ for $0<p\leq 1$ assuming a weaker $L^{s}-$type H\"ormander condition on the kernel.…

We establish the validity of a strong unique continuation property for weakly coupled elliptic systems, including competitive ones. Our proof exploits the system structure and uses Carleman estimates. We apply this result to obtain some…

This paper mainly addresses the strong unique continuation property for the electromagnetic Schr\"{o}dinger operator with complex-valued coefficients. Appropriate multipliers with physical backgrounds have been introduced to prove a priori…

We introduce here a general framework for studying continued fraction expansions for complex numbers and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial…

Given a Hermitian vector bundle over an infinite weighted graph, we define the Laplacian associated to a unitary connection on this bundle and study the essential self-adjointness of a perturbation of this Laplacian by an operator-valued…

In this short note we provide a quantitative version of the classical Runge approximation property for second order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these…

We give sharp two-sided estimates of the semigroup generated by the fractional Laplacian plus the Hardy potential on $\mathbb{R}^d$, including the case of the critical constant. We use Davies' method back-to-back with a new method of…

The purpose of this paper is to study the unique continuation property for a Schr\"odinger-type equation $ \bar\partial u = Vu$ on a domain in $\mathbb C^n$, where the solution $u$ may be a scalar function, or a vector-valued function.…

In this work, we study the higher differentiability of solutions to the inhomogeneous fractional $p$-Laplace equation under different regularity assumptions on the data. In the superquadratic case, we extend and sharpen several previous…

Let L be a Schr\"odinger operator of the form L=-\Delta+V, where the nonnegative potential V satisfies a reverse H\"older inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted H\"older…

In this paper we give log-convexity properties for solutions to discrete Schr\"odinger equations with different discrete versions of Gaussian decay at two different times. For free evolutions, we use complex analysis arguments to derive…

We study existence, regularity, and qualitative properties of solutions to linear problems involving higher-order fractional Laplacians $(-\Delta)^s$ for any $s>1$. Using the nonlocal properties of these operators, we provide an explicit…

Strong Feller property and irreducibility are study for a class of non-linear monotone stochastic partial differential equations with multiplicative noise. H\"older continuity of the associated Markov semigroups are discussed in some…

We obtain unique continuation results for Schrodinger equations with time dependent gradient vector potentials. This result with an appropriate modification also yields unique continuation properties for solutions of certain nonlinear…

In this paper, Morgan type uncertainty principle and unique continuation properties of abstract Schr\"odinger equations with time dependent potentials in vector-valued classes are obtained. The equation involves a possible linear operators…

In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric and magnetic potentials. Under suitable…

We calculate the regional fractional Laplacian on some power function on an interval. As an application, we prove Hardy inequality with an extra term for the fractional Laplacian on the interval with the optimal constant. As a result, we…