MMN-66
On the inf-type extremality solutions to Hamilton-Jacobi equations, their regularity properties, and some generalizations
Abstract
The extremality problem representation of the Lax type is studied in detail for some class of Hamilton-Jacobi equations in the many-dimensional case. The regularity properties of solutions of the Cauchy problem in the class of convex lower semicontinuous functions are established.
<p>A generalisation to a wider class of functions is obtained. The Hamilton-Jacobi equation on the sphere is considered, and its exact solutions are found in terms of a Lax type extremality problem. Some generalisation of the results for the general case of many-dimensional Hamilton-Jacobi equations is obtained by using the Fan-Brouwder fixed point techniques in a Banach space.
Vol. 4 (2003), No. 2, pp. 157-180
DOI: 10.18514/MMN.2003.66