Martin Ulmer

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math.AP2026

Nontangential Maximal Function estimates for the elliptic Mixed Boundary Value Problem with variable coefficients

Hongjie Dong, Martin Ulmer

We consider an elliptic operator $L$ with variable, merely bounded, and measurable coefficients on a Lipschitz domain, and study solutions to $Lu = 0$ that attain given Neumann and D…

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 solvabilit…

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…

Nontangential Maximal Function estimates for the elliptic Mixed Boundary Value Problem with variable coefficients

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

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 $\partial_{t} A$