This text examines the singularity problem for solutions of elliptic and parabolic quasilinear equations of second order.
PART I - ELLIPTIC EQUATIONS
Chapter I: Serrin's theory of
singularities: The linear equations, Removable singularities for quasilinear
equations, The characterisation of isolated singularities;
Chapter 2:
Semilinear equations with superlinear absorption: Removable singularities,
The isotropy theorems, The classification theorem, Anisotropic singularities,
Asymptotic behaviour and the connexion problem;
Chapter 3: Semilinear
equations with superlinear source: The radial case - Emden-Fowler equations,
The weakly superlinear case, The strongly superlinear case, The cirtical
Sobolev exponent case;
Chapter 4: Boundary singularities for semilinear
equations: Removable singularities, The classification theorems;
Chapter 5:
Quasilinear equations with source or absorption: Removable singularities,
Quasilinear equations with absorption, Quasilinear equations with sources.
PART II - PARABOLIC EQUATIONS
Chapter 6: Singularities of parabolic
equations: Removable singularities, Isolated singularities and isotropy
results, The classification theorems;
Chapter 7: Blow-up of parabolic
equations: Local and global existence, Single point blow-up, More general
blow-up.
Veron, Laurent
