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Extension theorems for solutions to over-determined systems of partial differential equations
Ehrenpreis has shown that, under suitable conditions, an infinitely differentiable solution to an overdetermined system of linear partial differentiable operators with constant coefficients has an extension across the ...
Numerical solution of a parabolic equation with unusual boundary conditions
The problem considered is that of a parabolic equation with space variables in a rectangle D. It is given that the normal derivative of the solution is zero on three sides of D and that the solution is a function of time ...
Some relations among Orlicz spaces
In this paper it is shown that for the study of Orlicz spaces the condition that a Young's function A be convex can be replaced by the more general (and more convenient) condition that A(x)/x be non-decreasing. Some ...
Global Regularity and Finite-time Blow-up in Model Fluid Equations
Determining the long time behavior of many partial differential equations modeling fluids has been a challenge for many years. In particular, for many of these equations, the question of whether solutions exist for all ...
Estimates for singular integrals
In a paper by Calderon and Zygmund some properties of a certain kind of singular integral are established, and these results are applied to particular fundamental solutions arising in partial differential equations. Jones ...
The problem of Plateau
Linear dimensions of (written el) P and LP spaces
Isomorphisms between Lq and Lp spaces exist for some ratios between p and q. For some of other ratios between p and q, no isomorphism exists. Similar results exist for Lp and Lq.