Christoph Schwerdt

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math.AP2026

Ultracontractivity of heat semigroups with non-local Robin boundary conditions via two-sided bounds for a positive eigenfunction

Christoph Schwerdt

We study heat semigroups on bounded Lipschitz domains $Ω \subset R^{d}$ with dimension $d > 2$ under non-local Robin boundary conditions. The boundary operator $B \in \mathca…

math.AP2026

Ultracontractivity of Heat semigroups in $L^{2} (Ω)$ with non-local Robin boundary conditions using Nash's inequality

Christoph Schwerdt

We study heat equations $\frac{\partial u}{\partial t} - div (A \nabla u) = 0$ on bounded Lipschitz domains $Ω$ in $R^{d}$ for $d \in \mathbb{N…

math.AP2026

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $L^{2} (R^{n})$ using Log-Sobolev-inequalities and duality arguments

Christoph Schwerdt, Ilham Ouelddris

We present a class of potentials $q : R^{n} \to (0, \infty)$ that implies the weighted Schrödinger semigroup $φ^{- 1} e^{- t H} φ$ to map a weighted Lebesgue funct…

math.AP2026

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $L^{2} (R^{n})$ by Logarithmic Sobolev inequalities

Christoph Schwerdt, Alexander Mill, Dirk Hundertmark

In the first part of this article we present a growth condition on the potential $q$ in the Schrödinger operator $H = - Δ + q (x)$ in $L^{2} (R^{n})$ that…

Ultracontractivity of heat semigroups with non-local Robin boundary conditions via two-sided bounds for a positive eigenfunction

Ultracontractivity of Heat semigroups in L2(Ω) with non-local Robin boundary conditions using Nash's inequality

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in L2(Rn) using Log-Sobolev-inequalities and duality arguments

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in L2(Rn) by Logarithmic Sobolev inequalities

Ultracontractivity of Heat semigroups in $L^{2} (Ω)$ with non-local Robin boundary conditions using Nash's inequality

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $L^{2} (R^{n})$ using Log-Sobolev-inequalities and duality arguments

Intrinsic Ultracontractivity for a class of Schroedinger Semigroups in $L^{2} (R^{n})$ by Logarithmic Sobolev inequalities