MA 3065 Study Guide - Final Guide: Viscosity Solution, Uniform Convergence, Lipschitz Domain

• School: Minneapolis College of Art and Design
• Department: Filmmaking-Sound
• Course: MA 3065
• Professor: p

Document Summary

Note: please choose a paper for your term end project/presentation by friday oct 5. Math 8590 homework 2 (due friday oct 5) Please hand in your solution to 1 problem from those below. 1. (a) let u, v usc(u ). H(d2w, dw, w, x) 0 in u. (1) Show that w(x) := max{u(x), v(x)} is a viscosity solution of (1) (i. e. , the pointwise maximum of two subsolutions is again a subsolution). (b) let u, v lsc(u ). Suppose that w := u and w := v are viscosity solutions of. H(d2w, dw, w, x) 0 in u. (2) Show that w(x) := min{u(x), v(x)} is a viscosity solution of (2): for each k n, let uk c(u ) be a viscosity solution of. H(d2uk, duk, uk, x) = 0 in u. Suppose that uk u locally uniformly on u (this means uk u uniformly on every. H(d2u, du, u, x) = 0 in u.