Regularity of solutions to infinitely degenerate elliptic equations with rough coefficients

Mardi 27 juin 15:00-16:00 - Cristian Rios - University of Calgary

Résumé : We obtain local boundedness and maximum principles for weak solutions to certain infinitely degenerate elliptic divergence form inhomogeneous equations, and also Hölder continuity of weak solutions to homogeneous equations.
The proofs are based on subrepresentation inequalities for the associated control geometries, which allow us to obtain Poincaré and Orlicz Sobolev a priori estimates.
We also apply our results to obtain weak hypoellipticity of certain infinitely degenerate quasiliear equations.
This is a preliminary report on ongoing work with L.Korobenko, R.Shen and E. Sawyer

Lieu : Petit amphi

Regularity of solutions to infinitely degenerate elliptic equations with rough coefficients  Version PDF