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J J Kohn

Publications and source records attributed to J J Kohn.

7 recordsLinked to original sources
PubMed1977

Sufficient conditions for subellipticity on weakly pseudo-convex domains.

Herein is outlined a method for studying a priori estimates by using the theory of ideals of functions. With this method a criterion is obtained for subelliptic estimates for the delta-Neumann problem. In case the boundary is real analytic, the theory of ideals of real-analytic functions gives a geometric interpretation of the criterion. For forms of type (p,n - 1), in which n is the complex dimension of the domain, we obtain necessary and sufficient conditions for subellipticity on pseudo-convex domains. The study of propagation of singularities for delta leads one to conjecture that, for pseudo-convex domains, with real-analytic boundaries, subellipticity for (p,q)-forms holds if and only if there are no complex-analytic varieties of dimension greater than or equal to q in the boundary. The methods described here give results concerning the sufficiency of the condition in this conjecture.

Journal Article↗
PubMed1975

Necessary and sufficient conditions for solvability of the Lewy equation.

We find the necessary and sufficient conditions for the local solvability of Lewy's equation, ([unk]/[unk]z + īz [unk]/[unk]t) u = f. If R(3) is realized as the boundary of the generalized "upper-half-space" in C(2), then the conditions are, near a point P [unk] R(3), the analytic continuability of the Cauchy-Szegö integral of f past P. In case the sufficient condition is satisfied, solutions are found that satisfy optimal regularity properties. Various generalizations are also given.

Journal Article↗
PubMed1974

Subellipticity on pseudo-convex domains with isolated degeneracies.

Previous work has lead the author to conjecture necessary and sufficient conditions for the subellipticity of the [unk]-Neumann problem on pseudoconvex domains. Here we outline a general method which reduces the problem of subellipticity to inequalities between germs of C(infinity) functions. We then describe how this method can be applied to prove the sufficiency of the conditions on domains whose boundaries have an isolated set of points on which the Levi form degenerates and such that in a neighborhood of these points the boundary is real analytic.

Journal Article↗
PubMed1972

The [unk]-Neumann Problem on (Weakly) Pseudo-Convex Two-Dimensional Manifolds.

When the Levi-form vanishes at boundary points of a pseudo-convex manifold, more delicate invariants are required to describe the function theoretic properties of the manifold. These are introduced here; the proof of the main theorem and other results, which will be described in more detail elsewhere, are described.

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