Regularity for Hamilton-Jacobi equations via approximation

Bum Il Hong
1995 Bulletin of the Australian Mathematical Society  
REGULARITY FOR HAMILTON-JACOBI EQUATIONS VIA APPROXIMATION BUM I I HONG We prove new regularity results for solutions of first-order partial differential equations of Hamilton-Jacobi type posed as initial value problems on the real line. We show that certain spaces determined by quasinorms related to the solution's approximation properties in C(R) by continuous, piecewise quadratic polynomial functions are invariant under the action of the differential equation. As a result, we show that
more » ... ns of Hamilton-Jacobi equations have enough regularity to be approximated well in C(R) by moving-grid finite element methods. The preceding results depend on a new stability theorem for Hamilton-Jacobi equations in any number of spatial dimensions. Received 6 April 1994 This paper was written after extensive conversation with B. Lucier and J. Douglas, Jr. at Purdue University. I am deeply indebted to them. I also thank R. DeVore at the University of South Carolina for his nice suggestions. Copyright Clearance Centre, Inc. Serial-fee code: 0004-9729/95 $A2.00+0.00.
doi:10.1017/s0004972700014052 fatcat:arnoqydpcrd5foyszqeys4pl4u