$B^q$ for parabolic measures

Caroline Sweezy

Displaying similar documents to “ $B^{q}$ for parabolic measures”

The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation

Neil Watson (2000)

Annales Polonici Mathematici

Similarity:

Let L be a second order, linear, parabolic partial differential operator, with bounded Hölder continuous coefficients, defined on the closure of the strip $X = ℝ^{n} \times] 0, a [$ . We prove a representation theorem for an arbitrary $C^{2, 1}$ function, in terms of the fundamental solution of the equation Lu=0. Such a theorem was proved in an earlier paper for a parabolic operator in divergence form with $C^{\infty}$ coefficients, but here much weaker conditions suffice. Some consequences of the representation theorem, for the...

Estimates of Green functions and their applications for parabolic operators with singular potentials

Lotfi Riahi (2003)

Colloquium Mathematicae

Similarity:

We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a $C^{1, 1}$ cylindrical domain Ω. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.

The Wolff gradient bound for degenerate parabolic equations

Tuomo Kuusi, Giuseppe Mingione (2014)

Journal of the European Mathematical Society

Similarity:

The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of $p$ -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.

Boundary estimates for certain degenerate and singular parabolic equations

Benny Avelin, Ugo Gianazza, Sandro Salsa (2016)

Journal of the European Mathematical Society

Similarity:

We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic $p$ -Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part $S_{T}$ of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of...

The $L^{p}$ solvability of the Dirichlet problems for parabolic equations

Xiang Tao (2000)

Studia Mathematica

Similarity:

For two general second order parabolic equations in divergence form in Lip(1,1/2) cylinders, we give a criterion for the preservation of $L^{p}$ solvability of the Dirichlet problems.

Absolute continuity for elliptic-caloric measures

Caroline Sweezy (1996)

Studia Mathematica

Similarity:

A Carleson condition on the difference function for the coefficients of two elliptic-caloric operators is shown to give absolute continuity of one measure with respect to the other on the lateral boundary. The elliptic operators can have time dependent coefficients and only one of them is assumed to have a measure which is doubling. This theorem is an extension of a result of B. Dahlberg [4] on absolute continuity for elliptic measures to the case of the heat equation. The method of...

On admissibility for parabolic equations in ℝⁿ

Martino Prizzi (2003)

Fundamenta Mathematicae

Similarity:

We consider the parabolic equation (P) $u_{t} - Δ u = F (x, u)$ , (t,x) ∈ ℝ₊ × ℝⁿ, and the corresponding semiflow π in the phase space H¹. We give conditions on the nonlinearity F(x,u), ensuring that all bounded sets of H¹ are π-admissible in the sense of Rybakowski. If F(x,u) is asymptotically linear, under appropriate non-resonance conditions, we use Conley’s index theory to prove the existence of nontrivial equilibria of (P) and of heteroclinic trajectories joining some of these equilibria. The results obtained...

Parabolic Marcinkiewicz integrals on product spaces and extrapolation

Mohammed Ali, Mohammed Al-Dolat (2016)

Open Mathematics

Similarity:

In this paper, we study the the parabolic Marcinkiewicz integral [...] MΩ,hρ1,ρ2 $ℳ_{Ω, h}^{ρ_{1,} ρ_{2}}$ on product domains Rn × Rm (n, m ≥ 2). Lp estimates of such operators are obtained under weak conditions on the kernels. These estimates allow us to use an extrapolation argument to obtain some new and improved results on parabolic Marcinkiewicz integral operators.

Parabolic measure on domains of class Lip $\frac{1}{2}$

Robert Kaufman, Jang-Mei Wu (1988)

Compositio Mathematica

Similarity:

The Calderón-Zygmund theorem and parabolic equations in $L P (ℝ, C^{2 + α})$ -spaces

Nicolai V. Krylov (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

A Banach-space version of the Calderón-Zygmund theorem is presented and applied to obtaining apriori estimates for solutions of second-order parabolic equations in $L_{p} (ℝ, C^{2 + α})$ -spaces.

Cauchy-Dirichlet problem in Morrey spaces for parabolic equations with discontinuous coefficients

Dian K. Palagachev, Maria A. Ragusa, Lubomira G. Softova (2003)

Bollettino dell'Unione Matematica Italiana

Similarity:

Let $Q_{T}$ be a cylinder in $R^{n + 1}$ and $x = (x^{'}, t) \in R^{n} \times R$ . It is studied the Cauchy-Dirichlet problem for the uniformly parabolic operator $\{\begin{matrix} u_{t} - \overset{n}{\sum_{i, j = 1}} a^{i j} (x) D_{i j} u = f (x) & q.o. in Q_{T}, \\ u (x) = 0 & su \partial Q_{T}, \end{matrix}$ in the Morrey spaces $W_{p, λ}^{2, 1} (Q_{T})$ , $p \in (1, \infty)$ , $λ \in (0, n + 2)$ , supposing the coefficients to belong to the class of functions with vanishing mean oscillation. There are obtained a priori estimates in Morrey spaces and Hölder regularity for the solution and its spatial derivatives.

Homogenization of a linear parabolic problem with a certain type of matching between the microscopic scales

Pernilla Johnsen, Tatiana Lobkova (2018)

Applications of Mathematics

Similarity:

This paper is devoted to the study of the linear parabolic problem $ε \partial_{t} u_{ε} (x, t) - \nabla \cdot (a (x / ε, t / ε^{3}) \nabla u_{ε} (x, t)) = f (x, t)$ by means of periodic homogenization. Two interesting phenomena arise as a result of the appearance of the coefficient $ε$ in front of the time derivative. First, we have an elliptic homogenized problem although the problem studied is parabolic. Secondly, we get a parabolic local problem even though the problem has a different relation between the spatial and temporal scales than those normally giving rise to parabolic...

Displaying similar documents to “ B q for parabolic measures”

Displaying similar documents to “ $B^{q}$ for parabolic measures”