Abstract approach to non homogeneous Harnack inequality in doubling quasi metric spaces

作者：Guidi Chiara; Montanari Annamaria^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2018, 169: 130-162.

DOI：10.1016/j.na.2017.12.009

• Invariant Harnack inequality
• Double ball property
• Critical density property
• Power decay property
• Doubling quasi-metric spaces
• Non divergence subelliptic PDEs with measurable coefficients
• Subelliptic equations
• Grushin vector fields
• Carnot-Caratheodory metric

We develop an abstract theory to obtain Harnack inequality for non homogeneous PDEs in the setting of quasi metric spaces. The main idea is to adapt the notion of double ball and critical density property given by Di Fazio, Gutierrez, Lanconelli, taking into account the right hand side of the equation. Then we apply the abstract procedure to the case of subelliptic equations in non divergence form involving Grushin vector fields and to the case of X-elliptic operators in divergence form.

• 出版日期2018-4