THIRD SEMESTER
Nonlinear PDEs (CM615)
CM615: Nonlinear PDEs
Prof. Vicenţiu Rădulescu
The maximum principles of Hopf and Alexandrov-Bakelman. Maximum principles for nonlinear differential equations. Applications: Serrin’s theorem (overdetermined problems), positive solutions of boundary value problems. Blow-up boundary solutions: existence and asymptotic analysis of solutions.
Non-existence results for semilinear and quasilinear problems: the Pokhozaev identity for star-shaped domains.
Radial symmetry of solutions. The moving plane method and the Gidas-Ni-Nirenberg theorem.
Nonlinear operator theory methods: mappings on finite-dimensional spaces, Nemytskii operators, pseudo-monotone operators. Applications to PDEs.
Bibliography
V. Barbu,
Partial Differential Equations and Boundary Value Problems, Mathematics and its Applications
, vol. 441, Kluwer, 1998.
H. Brezis and L. Nirenberg,
Nonlinear Functional Analysis and Applications to Partial Differential Equations
, in preparation.
L. Evans,
Partial Differential Equations
, Graduate Studies in Mathematics, vol. 19, Amer. Math. Soc., 1998.
J. Jost,
Partial Differential Equations
, Springer Verlag, 2002.
M. Renardy and R. Rogers,
An Introduction to Partial Differential Equations
, Springer Verlag, 1996.