We study global regularity properties of invariant measures associated with second order differential operators in $\R^N$. Under suitable conditions, we prove global boundedness of the density, Sobolev regularity, a Harnack inequality and pointwise upper and lower bounds. Many local regularity properties are known for invariant measures, even under very weak conditions on the coefficients, see e.g. [MR1876411 (2002m:60117)]. On the other hand, to our knowledge the only available results dealing with global regularity are [MR1351647 (96m:28015)] and [MR1391637 (98d:60120)], which have been the starting point of our investigation. The proofs relies upon Lyapunov functions and Moser's iteration techniques.
Global properties of invariant measures
RHANDI, Abdelaziz
2005
Abstract
We study global regularity properties of invariant measures associated with second order differential operators in $\R^N$. Under suitable conditions, we prove global boundedness of the density, Sobolev regularity, a Harnack inequality and pointwise upper and lower bounds. Many local regularity properties are known for invariant measures, even under very weak conditions on the coefficients, see e.g. [MR1876411 (2002m:60117)]. On the other hand, to our knowledge the only available results dealing with global regularity are [MR1351647 (96m:28015)] and [MR1391637 (98d:60120)], which have been the starting point of our investigation. The proofs relies upon Lyapunov functions and Moser's iteration techniques.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
