Martin Ulmer

collaborators

8 papers

math.AP2026

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

Martin DindoÅ¡, 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.AP2026

Failure of CalderÃ³n-Zygmund estimates for degenerate elliptic PDEs with $A_{p}$ -weights when $p > 2$

Armin Schikorra, Martin Ulmer

We use convex integration techniques to provide examples of failure of weighted CalderÃ³n-Zygmund estimates for degenerate linear elliptic PDEs when the weights are in $A_{p}$ , $p >…

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

Perturbation theory for the parabolic Regularity and Neumann problem

Martin Ulmer

We show small and large Carleson perturbation results for the parabolic Regularity boundary value problem with boundary data in $L ˙_{1, 1/2}^{p}$ and small Carelson perturbation…

math.AP2025

Solvability of the Dirichlet problem for a new class of elliptic operators

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 we…

The Lp regularity problem for parabolic operators with transversally independent coefficients

Failure of CalderÃ³n-Zygmund estimates for degenerate elliptic PDEs with Ap​-weights when p>2

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

Perturbation theory for the parabolic Regularity and Neumann problem

Solvability of the Dirichlet problem for a new class of elliptic operators

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

Failure of CalderÃ³n-Zygmund estimates for degenerate elliptic PDEs with $A_{p}$ -weights when $p > 2$

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