3 citations · 7 across the 8 of their papers we have counts for
7 papers · 1 filter
Null form estimates for (1/2,1/2) symbols and local existence for a quasilinear Dirichlet-wave equation
Hart Smith, Christopher D. Sogge
The authors show that bilinear estimates for null forms hold for Dirichlet-wave equations outside of convex obstacle. This generalizes results for the Euclidean case of Klainerman…
Weighted Strichartz estimates and global existence for semilinear wave equations
V. Georgiev, Hans Lindblad, Christopher D. Sogge
We prove certain weighted Strichartz estimates and use these to prove a sharp theorem for global existence of small amplitude solutions of , thus verifying the so…
Averages over curves with torsion
Daniel Oberlin, Hart Smith, Christopher D. Sogge
We establish Sobolev mapping properties for averages over certain curves in , which improve upon the estimates obtained by interpolation.
Global Strichartz estimates for nontrapping perturbations of the Laplacian
Hart Smith, Christopher D. Sogge
The authors prove global Strichartz estimates for compact perturbations of the wave operator in odd dimensions when a non-trapping assumption is satisfied.
Concerning Nikodym-type sets in 3-dimensional curved spaces
Christopher D. Sogge
We obtain estimates for maximal functions that arise when one studies Nikodym-type sets. We also formulate a curvature condition that allows favorable estimates for these maximal f…
Negative results for Nikodym maximal functions and related oscillatory integrals in curved space
William Minicozzi, Christopher D. Sogge
We expand on counterxamples of Bourgain showing how Nikodym maximal estimates and oscillatory integral estimates can break down in the non-Euclidean case. Our examples show the rol…