Related papers: A strong unique continuation result for the Baouen…

We prove that for elliptic and canceling linear differential operators $\mathbb{B}$ of order $n$ on $\mathbb{R}^n$, continuity of a map $u$ can be inferred from the fact that $\mathbb{B} u$ is a measure. We also prove strict continuity of…

Given a bounded Lipschitz domain $\omega\subset\mathbb{R}^{d-1}$ and a lower semicontinuous function $W:\mathbb{R}^N\to\mathbb{R}_+\cup\{+\infty\}$ that vanishes on a finite set and that is bounded from below by a positive constant at…

We prove, under certain conditions, the existence of zeros for a weakly continuous operator on a paracompact topological space into the dual of a Banach space.

Based on the three-ball inequality and the doubling inequality established in [23], we quantify the strong unique continuation established by Koch and Tataru [21] for elliptic operators with unbounded lower-order coefficients. We also…

We study a class of fully nonlinear boundary-degenerate elliptic equations, for which we prove that u \equiv 0 is the only solution. Although no boundary conditions are posed together with the equations, we show that the operator degeneracy…

Denote by $[0,\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on…

We prove maximal regularity results in H\"older and Zygmund spaces for linear stationary and evolution equations driven by a large class of differential and pseudo-differential operators L, both in finite and in infinite dimension. The…

In this paper we prove an energy estimate with no loss of derivatives for a strictly hyperbolic operator with Zygmund continuous second order coefficients both in time and in space. In particular, this estimate implies the well-posedness…

A (fragment of a) process algebra satisfies unique parallel decomposition if the definable behaviours admit a unique decomposition into indecomposable parallel components. In this paper we prove that finite processes of the pi-calculus,…

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…

Let $L$ be a linear differential operator with constant coefficients of order $n$ and complex eigenvalues $\lambda_{0},...,\lambda_{n}$. Assume that the set $U_{n}$ of all solutions of the equation $Lf=0$ is closed under complex…

We revisit \cite[Theorem 6.3]{JK}. Following the main ideas used to prove this theorem, we establish a quantitative version of the strong unique continuation property for the Sch\"odinger operator with unbounded potential. We also show that…

In this paper we classify all positive extremal functions to a sharp weighted Sobolev inequality on the upper half space, which involves divergent operators with degeneracy on the boundary. As an application of the results, we can derive a…

This paper is devoted to various applications of Hardy-Sobolev type inequalities. We derive a new $L^2$ estimate for the $\bar{\partial}-$equation on ${\mathbb C}^n$ which yields a quantitative generalization of the Hartogs extension…

Let M be a connected Riemannian manifold and let D be a Dirac type operator acting on smooth compactly supported sections in a Hermitian vector bundle over M. Suppose D has a self-adjoint extension A in the Hilbert space of…

In this paper, we establish a Liouville theorem for solutions to the Lane Emden equation involving Baouendi Grushin operators. We focus on solutions that are stable outside a compact set. Specifically, we prove that when p is smaller than…

We establish that the Pauli operator describing a spin-1/2 two-dimensional quantum system with a singular magnetic field has, under certain conditions, an infinite-dimensional space of zero modes, possibly, both spin-up and spin-down,…

We consider the second order Cauchy problem $$u''+\m{u}Au=0, u(0)=u_{0}, u'(0)=u_{1},$$ where $m:[0,+\infty)\to[0,+\infty)$ is a continuous function, and $A$ is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It is…

We give sharp regularity conditions, ensuring the backward uniquess property to a class of parabolic operators.

We obtain uniqueness theorems for harmonic and subharmonic functions of a new type. They lead to new analytic extension criteria and new conditions for stability of operator semigroups in Banach spaces with Fourier type.