Singular solutions of nonlinear elliptic and parabolic equations

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This monograph explores trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations, focusing on the existence and properties of weak and entropy solutions for elliptic second-order equations and certain fourth-order equations with L1-data. It addresses the removability of singularities in solutions to elliptic and parabolic second-order equations in divergence form. The text examines both localized and nonlocalized singularly peaking boundary regimes for various classes of quasilinear parabolic second- and higher-order equations in divergence form. The work is intended for researchers and post-graduate students specializing in partial differential equations and nonlinear analysis. The contents include: - Nonlinear elliptic equations with L^1-data, covering second-order equations with L^1-data and fourth-order equations with strengthened coercivity. - Removability of singularities in quasilinear elliptic and parabolic equations, detailing solutions for both types and including quasilinear elliptic equations with coefficients from the Kato class. - Boundary regimes with peaking for quasilinear parabolic equations, discussing energy methods for localized regimes and functional inequalities in peaking regimes for higher-order equations, as well as nonlocalized regimes with singular peaking. The appendix provides formulations and proofs of auxiliary results, complemented by a bibliography.