On local solvability of pseudo-differential equations

Menikoff, A.

doi:10.1090/S0002-9939-1974-0338844-1

On local solvability of pseudo-differential equations
HTML articles powered by AMS MathViewer

by A. Menikoff

Proc. Amer. Math. Soc. 43 (1974), 149-154

DOI: https://doi.org/10.1090/S0002-9939-1974-0338844-1

PDF | Request permission

Abstract:

A sufficient condition for the local solvability of the equation ${u_t} - A(x,t,{D_x})u = f(x,t)$ is proved, where $A$ is a first order pseudo-differential operator with real symbol. This is a special case of the local solvability conjecture of Nirenberg and Treves.

References

Richard Beals and Charles Fefferman, On local solvability of linear partial differential equations, Ann. of Math. (2) 97 (1973), 482–498. MR 352746, DOI 10.2307/1970832
Lars Hörmander, Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math. (2) 83 (1966), 129–209. MR 233064, DOI 10.2307/1970473
P. D. Lax and L. Nirenberg, On stability for difference schemes: A sharp form of Gȧrding’s inequality, Comm. Pure Appl. Math. 19 (1966), 473–492. MR 206534, DOI 10.1002/cpa.3160190409
Louis Nirenberg and François Trèves, On local solvability of linear partial differential equations. I. Necessary conditions, Comm. Pure Appl. Math. 23 (1970), 1–38. MR 264470, DOI 10.1002/cpa.3160230102
L. Nirenberg and J. F. Treves, Remarks on the solvability of linear equations of evolution, Symposia Mathematica, Vol. VII (Convegno sulle Problemi di Evoluzione, INDAM, Rome, 1970 & Convegno sulle Equazioni Ipoellittiche e Spazi Funzionali, INDAM, Rome, 1971) Academic Press, London, 1971, pp. 325–338. MR 0333846