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In this paper we explain how the local tomography approach to tomographic problems can be extended to a wide range of situations including limited data problems, attenuated transforms, and generalized radon transforms. Numerical examples illustrate the use of local tomography applied to complete and limited data problems. Our analytic results are obtained through the use of microlocal analysis.

We prove a Phragmèn-Lindelöf theorem which yields the behavior at infinity of bounded solutions of Dirichlet problems for non-hyperbolic (e.g., elliptic, parabolic) quasilinear second-order partial differential equations in terms of particular solutions of appropriate ordinary differential equations.

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ABSTRACT. Let 0 be an open set in R2 which is locally convex at each point of its boundary except one, say (0,0). Under certain mild assumptions, the solution of a prescribed mean curvature equation on Q behaves as follows: All radial limits of the solution from directions in 12 exist at (0,0), these limits are not identical, and the limits from a certain half-space (H) are identical. In particular, the restriction of the solution to Q n H is the solution of an appropriate Dirichlet problem. Introduction.We consider here the behavior of a generalized solution of the equation for surfaces of prescribed mean curvature at an inner corner of the boundary where the solution is discontinuous. This work is a generalization of the previous work of the second author [8], which dealt with the minimal surface equation. It was shown there that all radial limits exist and that they are constant in directions coming from a half-space. Here we find that the same result holds for (nonparametric) surfaces of prescribed mean curvature.