Comparison theorems for elliptic and parabolic inequalities
Ezzat S. Noussair, Charles A. Swanson · Illinois Journal of Mathematics · 1974
A recent comparison theorem of Kurt Kreith [2] will be extended to quasi- linear elliptic and parabolic differential inequalities of second order.Accordingly, Kreith's theorem is eneralized in three directions at once.Our proof is extremely easy, reducin the proposition to the Hopf maximum prin- ciple (in the elliptic case [3, p. 67]) or the Friedman theorem (in the parabolic case [3, p. 174]).Our hypotheses are c, unlike Kreith's indirect hy- potheses that "the boundary problems are sufficiently regular so that certain resolvents can be represented as integral operators."Let L be the elliptic differential operator defined by L(is symmetric nd uniformly positive definite in G (uniform ellipticity con- dition).