Solvability of the \(\mathrm{L}^p\) Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph

Maximal functions, Littlewood-Paley theory (42B25) Initial-boundary value problems for second-order parabolic equations (35K20) Heat equation (35K05) A priori estimates in context of PDEs (35B45) Free boundary problems for PDEs (35R35) Harmonic analysis and PDEs (42B37)

Cites Work

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The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability
On an inverse type problem for the heat equation in parabolic regular graph domains
Caloric measure in parabolic flat domains
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Harmonic measure on locally flat domains
Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials
Behavior near the boundary of positive solutions of second order parabolic equations
Free boundary regularity for harmonic measures and Poisson kernels
A weak reverse Hölder inequality for caloric measure
Harmonic measure and Riesz transform in uniform and general domains
A free boundary problem for the parabolic Poisson kernel
On a parabolic symmetry problem
Symmetry theorems and uniform rectifiability
\(L^ 2\) solvability and representation by caloric layer potentials in time-varying domains
Coronizations and big pieces in metric spaces
Corona decompositions for parabolic uniformly rectifiable sets
Regularity of the Poisson kernel and free boundary problems
On blow-ups and the classification of global solutions to parabolic free boundary problems
Behavior near the boundary of positive solutions of second order parabolic equations. II
The Dirichlet problem for second order parabolic operators
Poisson kernel characterization of Reifenberg flat chord arc domains
The method of layer potentials for the heat equation in time-varying domains
Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets

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