You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.<\/p>\n
Speaker: Isaac Ohavi (Kyiv School of Economics)<\/p>\n
\u201d Strong Comparison Principle for Fully Nonlinear Partial differential equations with Hamiltonians Discontinuous in all Variables\u201d<\/p>\n
Abstract: In this talk, we establish a strong comparison principle for viscosity solutions of fully nonlinear elliptic equations driven by second-order Hamiltonians that may be discontinuous with respect to all variables (mainly measurable).
\nThe analysis relies only on a controlled superlinear growth in the gradient variable together with a structural monotonicity in the unknown, and requires neither ellipticity and the Ishii\u2019s lemma pioneered in Lions-Crandall theory, nor continuity.
\nThe proof is based on the construction of tailored viscosity test functions obtained as solutions of auxiliary eikonal-type equations.
\nThese functions compensate for the lack of regularity and allow for a fully local comparison argument despite the complete discontinuity of the Hamiltonian. This yields a robust comparison principle in open subsets of $\\mathbb{R}^N$.
\nAs a consequence, we prove the existence of continuous viscosity solutions via a $L^p$ Perron method adapted to discontinuous frameworks.
\nThe class of Hamiltonians covered includes linear and quasilinear equations with merely Borel measurable coefficients, as well as Hamilton\u2013Jacobi\u2013Bellman equations arising in stochastic control and differential games.<\/p>\n
Date: May 12, Tuesday
\nTime: 14:00-15:00,
\nPlace: SA141<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the Analysis Seminar organized by the Department of Mathematics. Speaker: Isaac Ohavi (Kyiv School of Economics) \u201d Strong Comparison Principle for Fully Nonlinear Partial differential equations with Hamiltonians Discontinuous in all Variables\u201d Abstract: In this talk, we establish a strong comparison principle for viscosity solutions [\u2026] <\/p>\n