Related papers: Doubling properties for second order parabolic equ…

We prove local higher integrability of the gradient of a weak solution to a degenerate parabolic double-phase system. This result comes with a reverse H\"older type estimate for the gradient. The proof is based on estimates in the intrinsic…

This paper is devoted to the existence and Lipschitz continuity of global conservative weak solutions in time for the modified two-component Camassa-Holm system on the real line. We obtain the global weak solutions via a coordinate…

We introduce Poincar\'e type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the underline measure.

Let $(X,\mathcal W)$ be a balayage space, $1\in \mathcal W$, or - equivalently - let $\mathcal W$ be the set of excessive functions of a Hunt process on a locally compact space $X$ with countable base such that $\mathcal W$ separates…

We establish the local H\"older regularity of the spatial gradient of bounded weak solutions $u\colon E_T\to\R^k$ to the non-linear system of parabolic type \begin{equation*} \partial_tu-\Div\Big(…

We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…

Using variational methods, we prove local higher integrability for the minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces. We assume the measure to be doubling and the underlying space to be such that a…

We develop a method to study the structure of the common part of the boundaries of disjoint and possibly non-complementary time-varying domains in $\mathbb{R}^{n+1}$, $n \geq 2$, at the points of mutual absolute continuity of their…

Veestraeten [1] recently derived inverse Laplace transforms for Laplace transforms that contain products of two parabolic cylinder functions by exploiting the link between the parabolic cylinder function and the transition density and…

We solve some open problems regarding diameter two properties within the class of Banach spaces of real-valued Lipschitz functions by using the de Leeuw transform. Namely, we show that: the diameter two property, the strong diameter two…

We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is $\mu (x) \frac{\partial u}{\partial t} - \Delta u = 0$ where $\mu$ can be positive, null and…

In this paper, we consider second order degenerate parabolic equations with complex, measurable, and time-dependent coefficients. The degenerate ellipticity is dictated by a spatial $A_2$-weight. We prove that having a generalized…

In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…

In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.

We obtain sharp two-sided heat kernel estimates on spaces with varying dimension, in which two spaces of general dimension are connected at one point. On these spaces, if the dimensions of the two constituent parts are different, the volume…

We study the local behavior of the elements of a specific energy class of functions, called the nonlocal parabolic ($p$-homogenous) De Giorgi class. First we carry on an analysis of their local boundedness under optimal tail conditions, and…

In this paper we continue the study on intrinsic Harnack inequality for non- homogeneous parabolic equations in non-divergence form initiated by the first author in [1]. We establish a forward-in-time intrinsic Harnack inequality, which in…

This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. In [11] rate of convergence results in…

In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric divergence form operators. We show that a certain optimal…

We characterize two-weight inequalities for certain maximal truncations of the Hilbert transform in terms of testing conditions on simpler functions. For 1<p<2 and two positive Borel measures u, v on R, we assume that u is doubling, and we…