Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail: Keywords: nonlinear elliptic equations and systems of high order; apriori estimates; singular solutions; regularity of solutions; qualitative properties of solutions; irregular problems.
Subject:
Scientific interests: nonlinear elliptic equations and systems of high order; a priori estimates; singular solutions; regularity of solutions; qualitative properties of solutions; irregular problems.
Main results: New class of a priori estimates for nonlinear elliptic equations and systems of high order was obtained — estimates in dual Morrey spaces. It made possible to establish solvability for nonlinear elliptic systems for wide class of right-hand parts. New scale of functional spaces — dual Morrey spaces — was constructed. Isolated singularities of solutions for nonlinear elliptic equations and systems of high order were investigated. If the growth of energy of solution near the singularity is less from some limit growth depends from the modules of ellipticity of system, than the order of singularity is the same as for one of singular solutions of polylaplasian. Under some restrictions to the modules of ellipticity the existence of fundamental solutions for nonlinear elliptic systems was established.
Main publications:
Kalita E. A. Razreshimost nelineinykh ellipticheskikh sistem v prostranstvakh slabee estestvennogo energeticheskogo // Izvestiya RAN. Ser. matem., 1997, 61(2), 53–80.
Kalita E. A. Dualnye prostranstva Morri // Doklady RAN, 1998, 361(4), 447–449.
Kalita E. A. Ob osobykh tochkakh reshenii nelineinykh ellipticheskikh uravnenii i sistem vysokogo poryadka // Matem. sbornik, 1993, 184(7), 117–143.
