Introduction to non linear elliptic PDEs

ECTS : 6

Volume horaire : 37.5

Description du contenu de l'enseignement :

• Existence of weak solutions of linear and nonlinear elliptic PDEs by variational methods
• Regularity of weak solutions to linear and nonlinear elliptic PDEs
• Maximum principles and applications
• Brouwer degree, Leray-Schauder degree, fixed-point theorems
• Local and global bifurcation theory applied to nonlinear elliptic PDEs

Bibliographie, lectures recommandées :

• L.C. Evans, Partial Differential equations (Graduate Studies in Mathematics 19, AMS).
• L. Nirenberg, Topics in Nonlinear Functional Analysis (Courant Lecture Notes Series 6, AMS).