L^p-L^q estimates of the heat kernels on graphs with applications to a parabolic system

2025/05/12 by Hu, Yuanyang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.07565

Abstract

Let G=(V, E) be a locally finite connected graph satisfying curvature-dimension conditions (CDE(n, 0) or its strengthened version CDE'(n, 0))) and polynomial volume growth conditions of degree m. We systematically establish sharp L^p-bounds and decay-type L^p-L^q estimates for heat operators on G, accommodating both bounded and unbounded Laplacians. The analysis utilizes Li-Yau-type Harnack inequalities and geometric completeness arguments to handle degenerate cases. As a key application, we prove the existence of global solutions to a semilinear parabolic system on G under critical exponents governed by volume growth dimension m.

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