Daniel Hauer

collaborators

5 papers

math.AP2026

Fundamental Gaps for the Dirichlet p-Laplacian on Convex Domains

Rui Chen, Daniel Hauer

We study the fundamental gap of the Dirichlet $p$ -Laplacian on bounded convex domains. We first prove the sharp one-dimensional estimate $Γ_{p} (I_{D}, V) \geq (p - 1) (2^{p} - 1) (π_{p} / D)^{p}$ , $I_D…

math.AP2026

Sharp Lifespan Dichotomies and Threshold Phenomena for Semilinear Heat Equations Driven by the Logarithmic Laplacian

Huyuan Chen, Rui Chen, Daniel Hauer +1

We investigate nonnegative mild solutions of $\partial_{t} u + (- Δ)^{l n} u = f (u)$ in $(0, T) \times R^{N}$ , with initial datum $u (0, \cdot) = μ u_{0}$ , $μ > 0$ . Unlike the classical and frac…

math.AP2026

The Conformal Fractional--Logarithmic Laplacian on the Sphere: Yamabe Problems and Sharp Inequalities

Huyuan Chen, Rui Chen, Daniel Hauer

In this paper, we introduce the conformal fractional--logarithmic Laplacian on the unit sphere, defined as the derivative of the conformal fractional Laplacian with respect to the…

math.AP2024

Existence of an extremal function of Sobolev critical embedding with an $α$ -homogeneous weight

Petr Gurka, Daniel Hauer

In our previous publication [{\em Calc. Var. Partial Differential Equations}, 60(1):Paper No. 16, 27, 2021], we delved into examining a critical Sobolev-type embedding of a Sobolev…

math.AP2024

Regularity and Separation for $p$ -Laplace operators

Daniel Hauer, Adam Sikora

We analyze $p$ -Laplace operators with degenerate elliptic coefficients. This investigation includes Grušin type $p$ -Laplace operators. We describe a \emph{separation phenomenon} in…

Fundamental Gaps for the Dirichlet p-Laplacian on Convex Domains

Sharp Lifespan Dichotomies and Threshold Phenomena for Semilinear Heat Equations Driven by the Logarithmic Laplacian

The Conformal Fractional--Logarithmic Laplacian on the Sphere: Yamabe Problems and Sharp Inequalities

Existence of an extremal function of Sobolev critical embedding with an α-homogeneous weight

Regularity and Separation for p-Laplace operators

Existence of an extremal function of Sobolev critical embedding with an $α$ -homogeneous weight

Regularity and Separation for $p$ -Laplace operators