THE ESTIMATES OF THE MAXIMUM FOR THE GENERALIZED SOLUTIONS OF ELLIPTIC AND PARABOLIC EQUATIONS
Xingyu Liang · Journal of Southwest China Normal University · 1985
Let G be a bounded domain in the n-dimensional Euclidean space En, W12(G)be the usual Snbolev's functional space. with the aid of the maximum principle for the generalized solution we prove the following. Theorem 1 Suppose u∈W12 (G) satisfies the equationwhere the functions aαβ(x) = aβα (x) are measurable on G and there exists a constant x≥1 such thatand λ 0 is a constant. Then there exists a constant 0 Kλ 1 independent of u and f0 such thatThe result can parallelly extend to uniformly parabolic equations in divergence form as well as to the eases of both non-uniformly elliptic and parabolic equations in divergence forom.