Related papers: The property of unique continuation for second ord…
We prove local quantitative estimates of unique continuation for solutions to parabolic equations: doubling properties and two-sphere one-cylinder inequalities.
We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted…
This paper investigates the existence, uniqueness, and regularity of solutions to evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. We also explore trace embedding and…
We consider a compact Riemann surface with a holomorphic involution, two marked fixed points of the involution and a divisor obeying an equation up to linear equivalence of divisors involving all this data. Examples of such data are Fermi…
We investigate the quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients. Quantitative unique continuation described by the vanishing order is a quantitative form of strong unique…
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis…
We prove a local unique continuation result for Schr\''odinger operators with time independent Lipschitz metrics and lower order terms which are Gevrey 2 in time and bounded in space. This implies global unique continuation from any open…
A classical result due to Bochner characterizes the classical orthogonal polynomial systems as solutions of a second-order eigenvalue equation. We extend Bochner's result by dropping the assumption that the first element of the orthogonal…
In this paper, we study the quantitative unique continuation property of the second-order elliptic operators under the vanishing Neumann boundary condition over $C^{1,\alpha}$ or convex domains in two dimensions. We establish the optimal…
The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated.…
As the most significant difference from parabolic equations, long-time or short-time behavior of solutions to time-fractional evolution equations is dominated by the fractional orders, whose unique determination has been frequently…
This paper presents existence and uniqueness results for a class of parabolic systems with non linear diffusion and nonlocal interaction. These systems can be viewed as regular perturbations of Wasserstein gradient flows. Here we extend…
We investigate the quantitative uniqueness of solutions to parabolic equations with lower order terms on compact smooth manifolds. Quantitative uniqueness is a quantitative form of strong unique continuation property. We characterize…
We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity…
We consider the time-harmonic Maxwell system in a domain with a generalized impedance edge-corner, namely the presence of two generalized impedance planes that intersect at an edge. The impedance parameter can be $0, \infty$ or a finite…
In this work we study first-order linear parabolic evolution PDEs over $\mathbb{R}^{d}\times\mathbb{R}$ and $\mathbb{R}^{d}\times\mathbb{R}^{+}$ comprising a spatial operator defined through a symbol function and a source term such that its…
We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown medium without active inputs. The goal is the simultaneous…
We give sharp regularity conditions, ensuring the backward uniquess property to a class of parabolic operators.
We establish the strong unique continuation property of fractional orders of linear elliptic equations with Lipschitz coefficients by establishing monotonicity of some Almgren-type frequency functional via an extension procedure.
We investigate quantitative unique continuation properties for discrete magnetic Schr{\"o}dinger operators in certain periodic graphs. This unique continuation property will be quantified through what is known in the literature as a Three…