The main focus of the present text is on two topics: (a) asymptotics of Green's kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions. The novel feature of these asympt…
There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems rema…
"Singular Elliptic Problems provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. The book is an elementary introduction to nonlinear elliptic partial differential equations, which arise in the research o…