The X{sub {theta}}{sup s} spaces and unique continuation for solutions to the semilinear wave equation
The aim of this paper is twofold. First, we initiate a detailed study of the so-called X{sub {theta}}{sup s} spaces attached to a partial differential operator. This include localization, duality, microlocal representation, subelliptic estimates, solvability and L{sup {rho}}(L{sup q}) estimates. Secondly, we obtain some theorems on the unique continuation of solutions to semilinear second order hyperbolic equations across strongly pseudo-convex surfaces. These results are proved using some new L{sup {rho}}{yields} L{sup q} Carleman estimates, derived using the X{sub {theta}}{sup s} spaces. Our theorems cover the subcritical case; in the critical case, the problem remains open. Similar results hold for higher order partial differential operators, provided that the characteristic set satisfies a curvature condition. 23 refs.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 437122
- Journal Information:
- Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 5-6 Vol. 21; ISSN 0360-5302; ISSN CPDIDZ
- Country of Publication:
- United States
- Language:
- English
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