Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systems

Details Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systems Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systems

2007-03-12

arxiv.org/abs/math/0703294v2

Mathematics

Analysis of PDEs

43 pages. This second version is largely the same as the first. The changes involve the correction of a number of errors, inco

Scientific paper

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.

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