Displaying similar documents to “The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation”

B q for parabolic measures

Caroline Sweezy (1998)

Studia Mathematica

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If Ω is a Lip(1,1/2) domain, μ a doubling measure on ∂ p Ω , ∂ / ∂ t - L i , i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures ω 0 , ω 1 have the property that ω 0 ∈ B q ( μ ) implies ω 1 is absolutely continuous with respect to ω 0 whenever a certain Carleson-type condition holds on the difference function of the coefficients of L 1 and L 0 . Also ω 0 ∈ B q ( μ ) implies ω 1 ∈ B q ( μ ) whenever both measures are center-doubling measures. This is B. Dahlberg’s result for elliptic measures...

The Wolff gradient bound for degenerate parabolic equations

Tuomo Kuusi, Giuseppe Mingione (2014)

Journal of the European Mathematical Society

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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.

On admissibility for parabolic equations in ℝⁿ

Martino Prizzi (2003)

Fundamenta Mathematicae

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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...

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

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Let Q T be a cylinder in R n + 1 and x = x ′ , t ∈ R n × R . It is studied the Cauchy-Dirichlet problem for the uniformly parabolic operator u t - ∑ i , j = 1 n a i ⁢ j ⁢ x ⁢ D i ⁢ j ⁢ u = f ⁢ x q.o. in  ⁢ Q T , u ⁢ x = 0 su  ⁢ ∂ ⁡ Q T , in the Morrey spaces W p , λ 2 , 1 ⁢ Q T , p ∈ 1 , ∞ , λ ∈ 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.