SynopsisLet 7 be a selfadjoint uniformly elliptic partial differential operator on a bounded domain in R", and let S be a (possibly indefinite) L°° multiplication operator. Estimates of the form ak + o(k) and ak + P + o(l) are sought for the eigenvalues ft(k) of kS -7 as k-* ±°°. A necessary and sufficient condition is also obtained for existence of linear eigencurves, i.e. p(k) = ok + ft.

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Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift.

a b s t r a c tThe lateral boundary differentiability with respect to x is shown for solutions of parabolic differential equations in nondivergence form on cylindrical convex domains.

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