Kovalevsky A.A., Skrypnik I.I., Shishkov A.E. Singular Solutions of Nonlinear Elliptic and Parabolic Equations

Walter de Gruyter GmbH, Berlin, Boston, 2016. — 449 p. — (De Gruyter Series in Nonlinear Analysis and Applications 24) — ISBN10: 3110315483.This monograph looks at several trends of investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions to these equations. It will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis.Nonlinear elliptic equations with L1-data
Nonlinear elliptic equations of the second order with L1-data
Nonlinear equations of the fourth order with strengthened coercivity and L1-data
Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order
Removability of singularities of the solutions of quasilinear elliptic equations
Removability of singularities of the solutions of quasilinear parabolic equations
Quasilinear elliptic equations with coefficients from the Kato class
Boundary regimes with peaking for quasilinear parabolic equations
Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations
Method of functional inequalities in peaking regimes for parabolic equations of higher orders
Nonlocalized regimes with singular peaking
Appendix: Formulations and proofs of the auxiliary results