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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A residue-type phenomenon and its applications to higher order nonlinear systems of Poisson type
Yifei Pan,Yuan Zhang +1 more
TL;DR: In this paper, a Residue-type phenomenon for the fundamental solution of the Laplacian was established and a higher order derivative formula for the Newtonian potential and its Holder estimates with a gain of two derivatives was derived.
Book ChapterDOI
Second Microlocalization Methods for Degenerate Cauchy—Riemann Equations
TL;DR: In this paper, a class of degenerate Cauchy-Riemann equations with respect to a hypersurface is studied and the second microlocalization with respect of a hypersuran surface is used to formulate and prove propagation and solvability results.
Journal ArticleDOI
Local solvability and hypoellipticity for operators with odd order characteristics
Gray B. Roberts,Paul R. Wenston +1 more
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On a parametrix in some weak sense of a first order linear partial differential operator with two independent variables
Journal ArticleDOI
Local solvability of partial differential operators on the Heisenberg group
TL;DR: In this article, the authors examined a class of partial differential operators for local solvability and showed that they are locally solvable if and only if the kernels of the ordinary differential operators P(iδx, ± x)* contain no Schwartz-class functions other than the zero function.
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.
Journal ArticleDOI
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.