Martin Ulmer

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20232026

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4 papers · 2 filters

math.AP2025

Equivalence between solvability of the Dirichlet and Regularity problem under an $L^{1}$ Carleson condition on $\partial_{t} A$

Martin Ulmer

We study an elliptic operator $L := - div (A \nabla \cdot)$ on the upper half space. It is known that solvability of the Regularity problem in $W ˙^{1, p}$ implies solvabili…

math.AP2025

The $L^{p}$ regularity problem for parabolic operators with transversally independent coefficients

Martin Dindoš, Jill Pipher, Martin Ulmer

In this paper, we fully resolve the question of whether the Regularity problem for the parabolic PDE $\partial_tu - \mbox{div}(A\nabla u)=0$ on the domain $\mathbb R^{n+1}_+\times\…

math.AP2025

The regularity problem with a weaker condition on only the transversal direction

Martin Ulmer

We study an elliptic operator $L := div (A \nabla \cdot)$ on the upper half space. It is known that if the matrix $A$ is independent in the transversal $t$ -direction, then the…

math.AP2025

Solvability of the Dirichlet problem using a weaker Carleson condition in the upper half plane

Martin Ulmer

We study an elliptic operator $L := div (A \nabla \cdot)$ on the upper half plane $R_{+}^{2}$ . There are several conditions on the behavior of the matrix $A$ in the trans…

Equivalence between solvability of the Dirichlet and Regularity problem under an L1 Carleson condition on ∂t​A

The Lp regularity problem for parabolic operators with transversally independent coefficients

The regularity problem with a weaker condition on only the transversal direction

Solvability of the Dirichlet problem using a weaker Carleson condition in the upper half plane

Equivalence between solvability of the Dirichlet and Regularity problem under an $L^{1}$ Carleson condition on $\partial_{t} A$

The $L^{p}$ regularity problem for parabolic operators with transversally independent coefficients