ON THE ANALYTICITY OF THE SOLUTIONS OF ANALYTIC NON-LINEAR ELLIPTIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS.*1
Charles B. Morrey · 2016
this part, we shall show that a solution of a strongly elliptic (in the sense of Nirenberg, [5]) analytic system, which possesses Dirichlet data which are analytic along an analytic portion of the boundary of its domain of definition,, can be extended analytically across that portion of the boundary. The analyticity of the solutions of general analytic elliptic systems on the interior of their domains of definition has been proved in Part I [4] where a more extensive introduction and bibliography are given. We number the sections of Part II serially after those of Part I. Avner Friedman [1] has recently extended the results of Parts I and II to obtain corresponding results for quasi-analytic systems and the still more general systems in which the oj belong to the M.,, classes of Mandelbrojt [3]. Since such a system remains analytic and strongly elliptic under an analytic transformation of the independent variables, we may choose anypoint on our portion of the boundary and transform the part of the~ domain and its boundary analytically onto that part of the hemisphere