01.01.02 (Differential equations, dynamical systems, and optimal control)
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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.
Biography
Graduated from Faculty of Mathematics of Donetsk State University in 1983. Ph.D. thesis was defended in 1989 (Institute of Applied Mathematics and Mechanics NAS Ukraine). Author of more than 30 papers.
In 1995 I was awarded the prize of National Academy of Sciences of Ukraine for joung scientiests for a series of papers on the singular solutions of nonlinear elliptic systems.
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.
E. A. Kalita, “Morrey Regularity of Nonlinear Elliptic Systems of High Order under Degeneration of Ellipticity”, Mat. Zametki, 72:2 (2002), 198–206; Math. Notes, 72:2 (2002), 177–184
1999
4.
E. A. Kalita, “Local properties of solutions of higher-order elliptic systems with double nonlinearity”, Mat. Zametki, 65:2 (1999), 314–317; Math. Notes, 65:2 (1999), 259–262
1997
5.
E. A. Kalita, “Solubility of non-linear elliptic systems in spaces that are weaker than the natural energy space”, Izv. RAN. Ser. Mat., 61:2 (1997), 53–80; Izv. Math., 61:2 (1997), 285–315
E. A. Kalita, “Compactness of the support and nonexistence of singularities for nonlinear elliptic systems of arbitrary order”, Sibirsk. Mat. Zh., 35:2 (1994), 327–339; Siberian Math. J., 35:2 (1994), 294–305
1993
9.
E. A. Kalita, “Asymptotic behavior of solutions of nonlinear elliptic systems at infinity”, Differ. Uravn., 29:4 (1993), 627–636; Differ. Equ., 29:4 (1993), 533–541
E. A. Kalita, “Conditions for the existence of a fundamental solution of quasilinear elliptic equations and higher-order systems with discontinuous coefficients”, Mat. Zametki, 54:6 (1993), 132–134; Math. Notes, 54:6 (1993), 1274–1276
11.
E. A. Kalita, “On singular points of solutions of nonlinear higher-order elliptic equations and systems”, Mat. Sb., 184:7 (1993), 117–143; Russian Acad. Sci. Sb. Math., 79:2 (1994), 315–334
E. A. Kalita, “Limit smoothness of solutions of second-order elliptic systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, no. 3, 10–17; Russian Math. (Iz. VUZ), 36:3 (1992), 8–15
1991
13.
E. A. Kalita, “Behavior of solutions of quasilinear elliptic systems at a nonregular boundary point”, Differ. Uravn., 27:5 (1991), 826–836; Differ. Equ., 27:5 (1991), 573–582
1989
14.
E. A. Kalita, “Regularity of solutions of second-order elliptic systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1989, no. 11, 37–46; Soviet Math. (Iz. VUZ), 33:11 (1989), 45–54
Dual Morrey spaces in nonlinear elliptic PDEs E. A. Kalita Conference on the Theory of Functions of Several Real Variables, dedicated to the 90th anniversary of O. V. Besov June 2, 2023 16:00
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