AN ASYMPTOTIC EXPANSION OF THE SOLUTION OF A SECOND ORDER ELLIPTIC EQUATION WITH PERIODIC RAPIDLY OSCILLATING COEFFICIENTS
E V Sevost'janova · Mathematics of the USSR-Sbornik · 1982
This paper studies the asymptotic behavior of the fundamental solution of the equation specified on the whole space , , as . The coefficients are periodic functions which satisfy the conditions of ellipticity, symmetry, and infinite smoothness.The main result is the construction of the asymptotics of in the form where is an arbitrary positive integer, the are homogeneous of degree in the first argument and periodic in the remaining arguments, and for the remainder term on the set , , the estimate holds, where the constants are independent of , , and .Bibliography: 9 titles.