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.
Guidi, C., Montanari, A. (2018). Abstract approach to non homogeneous Harnack inequality in doubling quasi metric spaces. NONLINEAR ANALYSIS, 169, 130-162 [10.1016/j.na.2017.12.009].
Abstract approach to non homogeneous Harnack inequality in doubling quasi metric spaces
Montanari, Annamaria
2018
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
