Bassanelli, Giovanni On a Hamilton-Jacobi equation. (English) Zbl 0704.35029 Rend. Semin. Mat. Univ. Padova 82, 99-114 (1989). Author’s summary: “We prove a theorem of existence and uniqueness for the problem: \[ \frac{\partial}{\partial u}\phi \frac{\partial}{\partial v}\phi +\sum a_{jk}(u,v,z)\frac{\partial}{\partial z_ j}\phi \frac{\partial}{\partial z_ k}\phi =0 \] with data: \(\phi (u,v,z,\eta)=z\cdot \eta\) for \(uv=0\), on a strip [0,U]\(\times {\bar {\mathbb{R}}}^+\times {\mathbb{R}}^ n\times {\dot {\mathbb{R}}}^ n\) where \(A=(a_{jk})\) is a \(C^{\infty}\), \(n\times n\), negative definite real matrix. Reviewer: J.Wloka MSC: 35F20 Nonlinear first-order PDEs 70H20 Hamilton-Jacobi equations in mechanics 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:existence; uniqueness PDFBibTeX XMLCite \textit{G. Bassanelli}, Rend. Semin. Mat. Univ. Padova 82, 99--114 (1989; Zbl 0704.35029) Full Text: Numdam EuDML References: [1] G. Bassanelli , On a characteristic Cauchy problem , Ann. Mat. Pura Appl. , ( IV ) CXLVII ( 1987 ), pp. 343 - 362 . MR 916714 | Zbl 0637.35016 · Zbl 0637.35016 · doi:10.1007/BF01762423 [2] J. Chazarain - A. Piriou , Problemes mixtes hyperboliques, in Hyperbolicity , Corso CIME 1976 , Liguori , 1977 . Zbl 0457.35053 · Zbl 0457.35053 [3] L. Hormander , The Analysis of Linear Partial Differential Operators , vol. 1 , Springer , 1973 . [4] J.B. Kogut - D. E. SOPER, Quantum electrodynamics in the infinite momentum frame , Phys. Rev. D , 1 ( 1970 ), p. 291 . [5] B.A. Neville - F. ROHRLICH, Quantum field theory of null planes , Nuovo Cimento A , 1 ( 1971 ), p. 625 . MR 289062 [6] B.A. Neville - F. ROHRLICH, Quantum electrodynamics of null planes and applications to lasers , Phys. Rev. D , 3 ( 1971 ), p. 1692 . [7] F. Treves , Introduction to Pseudo Differential and Fourier Integral Operators , vol. 1 , Plenum Press , 1980 . MR 597145 | Zbl 0453.47027 · Zbl 0453.47027 [8] F. Treves , Basic Linear Partial Differential Equations , Academic Press , 1980 . Zbl 0305.35001 · Zbl 0305.35001 [9] S. Weinberg , Dynamic at infinite momentum , Phys. Rev. , 150 ( 1966 ), p. 1313 . This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.