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Lp-Theory of degenerate-elliptic and parabolic operators of second order

  • Baoswan Wong-Dzung (a1)

Synopsis

We consider the formal operator given by

in the Banach space X = LP(Rn), 1<p<∞. The coefficients ajk(x), aj(x), and a(x) are real-valued functions, ajk ε C2(Rn) has bounded second derivatives, aj ε Cl(Rn) has bounded first derivatives, and aεL(Rn). Furthermore, we assume that the n × n matrix (ajk(x)) is symmetric and positive semidefinite (i.e. ajk(xjξk≧0 for all (ξ1,…,ξnRn and x ε Rn). We prove that the degenerate-elliptic differential operator given by –A and restricted to , the minimal realization of –A, is essentially quasi-m-dispersive in Lp(Rn), (hence that the minimal realization of +A is quasi-m-accretive) and that its closure coincides with the maximal realization of –A.

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