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math.PR2026
A Heat Kernel Expectation Approach to Boundary-Corrected Li--Yau Estimates for the Dirichlet Heat Equation
Li-Chang Hung
In this paper, we establish an explicit boundary-corrected Li--Yau type gradient estimate for positive solutions of the Dirichlet heat equation on the Euclidean half-space. The mai…
math.PR2026
A Variance Representation Formula for Hölder's Inequality
Li-Chang Hung
We establish an exact representation formula for the deficit in Hölder's inequality. Rather than estimating the deficit by auxiliary quantities, we show that it can be represented…