Related papers: Backward uniqueness for parabolic operators with n…

We prove the backward uniqueness for general parabolic operators of second order in the whole space under assumptions that the leading coefficients of the operator are Lipschitz and their gradients satisfy certain decay conditions. This…

We investigate the relation between the backward uniqueness and the regularity of the coefficients for a parabolic operator. A necessary and sufficient condition for uniqueness is given in terms of the modulus of continuity of the…

We prove uniqueness for backward parabolic equations whose coefficients are Osgood continuous in time for $t>0$ but not at $t=0$.

Using Bony's paramultiplication we improve a result obtained in in a previous paper for operators having coefficients non-Lipschitz-continuous with respect to $t$ but ${\mathcal C}^2$ with respect to $x$, showing that the same result is…

We prove logarithmic conditional stability up to the final time for backward-parabolic operators whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. The result complements previous achievements of Del…

In this paper we present an improvement of [Math. Ann. 345 (2009), 213--243], where the authors proved a result concerning continuous dependence for backward parabolic operators whose coefficients are Log-Lipschitz in $t$ and $C^2$ in $x$.…

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

In this paper, we establish strong backward uniqueness for solutions to sublinear parabolic equations of the type (1.1). The proof of our main result Theorem 1.1 is achieved by means of a new Carleman estimate and a Weiss type monotonicity…

In this paper, we study parabolic equations in divergence form with coefficients that are singular degenerate as some Muckenhoupt weight functions in one spatial variable. Under certain conditions, weighted reverse H\"{o}lder's inequalities…

The purpose of this short note is to show how it is possible to combine existing results in the literature to get the unique continuation from sets of positive measure for time dependent parabolic equations with Lipschitz principal part and…

It is shown that a function $u$ satisfying $|\partial_tu+\sum_{i,j}\partial_i(a^{ij}\partial_ju)|\leq N(|u|+|\nabla u|)$, $|u(x,t)|\leq Ne^{N|x|^2}$ in $\mathbb{R}^n_+\times[0,T]$ and $u(x,0)=0$ in $\mathbb{R}^n_+$ under certain conditions…

We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability…

We prove continuous dependence on Cauchy data for a backward parabolic operator whose coefficients are Log-Lipschitz continuous in time.

We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…

The aim of this article is to study the asymptotic behaviour for large times of solutions to a certain class of stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the…

We prove backward uniqueness for a class of ultraparabolic operators with coupled linear drift. The main difficulty is that the Fourier transform in the degenerate variables turns the coupled drift into a transport operator in the dual…

We find minimal regularity conditions on the coefficients of a parabolic operator, ensuring that no nontrivial solution tends to zero faster than any exponential.

In this work we determine the second-order coefficient in a parabolic equation from the knowledge of a single final data. Under assumptions on the concentration of eigenvalues of the associated elliptic operator, and the initial state, we…

We prove continuous dependence on initial data for a backward parabolic operator whose leading coefficients are Osgodd continuous in time. This result fills the gap between uniqueness and continuity results obtained so far.

We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal…