2003/01/30 by Nicolas Burq, Burq, Nicolas
Mathematics · #35P99 #58J40 #58J50 #81S10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35P99 #msc:58J40 #msc:58J50 #msc:81S10
paper · pdf · doi:10.48550/arxiv.math/0301349
10 pages
arxiv created 2003/01/30 · arxiv updated 2009/11/30
Consider M, a bounded domain in \mathbb Rd, which is a Riemanian manifold with piecewise smooth boundary and suppose that the billiard associated to the geodesic flow reflecting on the boundary acording to the laws of geometric optics is ergodic. We prove that the boundary value of the eigenfunctions of the Laplace operator with reasonable boundary conditions are asymptotically equidistributed in the boundary, extending previous results by Gérard, Leichtnam \citeGeLe93-1 and Hassel, Zelditch \citeHaZe02 obtained under the additional assumption of the convexity of M.