PDE seminar On the weak comparison principle for elliptic equations of mean curvature type

2010-11-29 16:30 - 2010-11-29 17:30
Faculty of Science Building #3 Room 202
Qing Liu (Department of Mathematics, The University of Tokyo)
We present some applications of the game-theoretic approach to
second-order PDEs. Our main topic is the weak comparison principle for a
stationary equation of mean curvature type in a general domain. We show a
counteresxample for the weak comparison theorem by picking special game
strategies and estimating game values. We also reveal general relationship
between the fattening phenomenon and the loss of comparison principles.