Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systems
Analysis of PDEs
2007-09-16 v2
Abstract
For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some system-dependent constant which is strictly less than 1 and, on the other hand, that for any system of the kind considered there is in fact a solution on a half-plane which fails to have nontangential limits at a set of boundary points of positive Hausdorff dimension.
Keywords
Cite
@article{arxiv.math/0703294,
title = {Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systems},
author = {Julian Gevirtz},
journal= {arXiv preprint arXiv:math/0703294},
year = {2007}
}
Comments
43 pages. This second version is largely the same as the first. The changes involve the correction of a number of errors, incorporation of some simplifications and more detailed proofs of a few of the propositions