Introduction to fully nonlinear parabolic equations

Cyril Imbert (1) , Luis Silvestre (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Department of Mathematics [Chicago]

These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations.

Mots clés: Parabolic equations; Schauder estimates; viscosity solutions; Perron's method; Ishii-Lions' method; Harnack inequality

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Luis Silvestre. Introduction to fully nonlinear parabolic equations. 2012. ⟨hal-00798300⟩