Partial results on extending the Hopf Lemma

In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a very partial answer. We write this paper to call attention to the problem

On Some Microlocal Properties of the Range of a Pseudo-Differential Operator of Principal Type

The purpose of this paper is to obtain microlocal analogues of results by L. H \"ormander about inclusion relations between the ranges of first order differential operators with coefficients in $C^\infty$ which fail to be locally solvable. Using similar techniques, we shall study the properties of the range of classical pseudo-differential operators of principal type which fail to satisfy condition $(\Psi)$.Comment: With 1 figure. Corrected typos. Rewrote parts of Section 2 to account for new language. Corrected an erroneous comment following Theorem 2.1

Holomorphic Approximation on Real Submanifolds of C^n

Paper by Ricardo Nirenber