Singularities of Solutions of Second-Order Quasilinear Equations
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This text examines the singularity problem for solutions of elliptic and parabolic quasilinear equations of second order.
Table of Contents
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.