On the zeros of solutions of a linear analytic partial differential equation of arbitrary order

V. I. Ruderfer


Abstract: This paper considers the question of the decay in a neighborhood of a zero on the boundary of a solution of a linear differential equation of any order with principal part consisting of an operator elliptic in the space variables. The coefficients of the equation are assumed to be analytic. An estimate is obtained of the solution of the Cauchy problem with data on a timelike surface in which the dependence on the dimensions of the support of the data is explicitly exhibited. The question of the admissible zeros on the boundary of the domain of definition is solved on the basis of the estimate obtained.
Bibliography: 7 titles.

UDC: 517.946

MSC: Primary 35B05, 35B45, 35G05; Secondary 35G10, 35J30

Received: 06.10.1978

 English version: Mathematics of the USSR-Sbornik, 1980, 37:3, 403–410

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