Dr. Igor Verbitsky’ s research focuses on harmonic analysis and nonlinear potential theory methods, and their applications to linear, quasilinear, and fully nonlinear equations with singular coefficients and data.
He studies weighted norm inequalities, existence, uniqueness, and regularity properties, global and local estimates of solutions, singularities and exceptional sets. His work has been published in Annals of Mathematics, Acta Mathematica, Inventiones Mathematicae, Communications on Pure and Applied Mathematics, Archive for Rational Mechanics and Analysis, Advances in Mathematics, Journal of Functional Analysis, Journal d'Analyse Mathematique, Journal fur die reine und angewandte Mathematik (Crelle's Journal), etc.
Education
1979 Ph.D., Kazan State University, Russia
Frequently Taught Courses
MATH1700 Calculus II
MATH 2300 Calculus III
MATH 8425 Complex Analysis I
MATH 8302 Topics in Harmonic Analysis
Research Interests
Harmonic Analysis, Partial Differential Equations, Potential Theory, Complex Analysis
MathSciNet Links
authored by Igor Verbitsky
Select Publications
Jaye, B., Verbitsky, I. (2013). The fundamental solution of nonlinear equations with natural growth terms. Annali della Scuola Normale Superiore di Pisa, 12, 93-139.
Jaye, B., Maz'ya, V., Verbitsky, I. (2013). Quasilinear elliptic equations and weighted Sobolev-Poincare inequalities with distributional weights. Advances in Mathematics, 232, 513-542.
Jaye, B., Verbitsky, I. (2012). Local and global behaviour of solutions to nonlinear equations with natural growth terms. Archive for Rational Mechanics and Analysis, 204, 627-681.
Ferrari, F., Verbitsky, I. (2012). Radial fractional Laplace operators and Hessian inequalities. Journal of Differential Equations, 253, 244-272.
Ferrari, F., Franchi, B., Verbitsky, I. (2012). Hessian inequalities and the fractional Laplacian. Journal fur die reine und angewandte Mathematik (Crelle's Journal) 667, 133-148.
Nguyen, Cong Phuc, Verbitsky, I. (2009). Singular quasilinear and Hessian equations and inequalities. Journal of Functional Analysis, 256, 1875-1906.
Nguyen, Cong Phuc, Verbitsky, I. (2008). Quasilinear and Hessian equations of Lane-Emden type. Annals of Mathematics, 168, 859-914.