Abstract
A solution u* of the second-order mildly nonlinear elliptic boundary-value problem Lu = F(u) in ..cap omega.., B/sub sigma/u = phi on par.delta ..cap omega.. is called classical if u* is an element of C(..cap omega..-bar)IC/sup sigma/(..cap omega..US)IC/sup 2/(..cap omega..), where U and I stand for union and intersection, S is the smooth part of the boundary, and sigma is 0 or 1 according as B/sub sigma/ is a zeroth- or first-order derivative boundary operator. The existence and stability of these classical solutions are studied. 2 figures. (RWR)
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