Journal ArticleDOI
On local solvability of linear partial differential equations—part II. Sufficient conditions†
Louis Nirenberg,François Treves +1 more
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This article is published in Communications on Pure and Applied Mathematics.The article was published on 1970-05-01. It has received 122 citations till now. The article focuses on the topics: First-order partial differential equation & Parabolic partial differential equation.read more
Citations
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Local solvability in top degree of the semilinear Kohn equation
TL;DR: In this article, the authors studied the local solvability problem for a class of semilinear equations whose linear part is the Kohn Laplacian, acting on top degree forms.
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Fundamental solutions of some degenerate operators
TL;DR: In this article, the authors modify the usual series computation for a parametrix of an elliptic operator and find a method that is applicable to some simple degenerate operators, such as D x + ixD y and D x 2 + x 2 D y 2 + cD y.
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Hypoellipticity of second order differential operators with sign-changing principal symbols
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An approximate positive part of a self-adjoint pseudo-differential operator. I
TL;DR: In this article, a self-adjoint pseudo-differential operator P =p(x, D) is constructed from its principal symbol, and the following properties are established: (i) F+F~=Id.
References
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Journal ArticleDOI
The Spectral Function of an Elliptic Operator
TL;DR: In this article, the authors obtained the best possible estimates for the remainder term in the asymptotic formula for the spectral function of an arbitrary elliptic (pseudo-)differential operator.
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Pseudo-Differential Operators
TL;DR: In this article, Second Order Elliptic Operators on a Compact Manifold without Boundary have been studied, as well as the Mixed Dirichlet-Cauchy Problem for Second Order Operators.