Gradient estimate and Universal bounds for semilinear elliptic equations on RCD$^*$(K,N) metric measure spaces

Autor:	Lu, Zhihao
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Metric Geometry
Druh dokumentu:	Working Paper
Popis:	We provide logarithmic gradient estimate and universal boundedness estimate for semilinear elliptic equations on RCD$^*(K,N)$, metric measure spaces. In certain case, these estimates are optimal even on RCD$^*(K,N)$ spaces with $K<0$. Two direct corollaries of these estimates are Harnack inequality and Liouville theorem. In addition to these estimates, we also establish relations among the universal boundedness estimate, the logarithmic gradient estimate, and Harnack inequality. Under certain conditions, even in wild setting, they are $\kappa$-equivalent on RCD$^*(0,N)$ spaces for any $\kappa>1$. Comment: arXiv admin note: text overlap with arXiv:2308.14026
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.14764 Zobrazit plný text záznamu View this record from Arxiv