Multilinear Square Functions and Partial Differential Equations
Copyright policy )Multilinear Square Functions and Partial Differential Equations
The purpose of this paper is to give detailed proofs of the results announced by the authors [Proc. Natl. Acad. Sci. USA 79, 5746-5750 (1982; Zbl 0501.35014)]. The first section deals with the basic multilinear estimates of Littlewood-Paley type that are needed for our applications. Roughly speaking, if the operator is k-linear, its norm is shown to be \(C^ k\) for an appropriate C. The operators considered arise naturally in several problems in partial differential equations. Here we present two applications. Another application is given by the authors [Ann. Math., II. Ser. 119, 121-141 (1984; Zbl 0551.35024)].
Systems of elliptic equations, general, Cauchy problem, General theory of partial differential operators, a priori estimates, multilinear estimates of Littlewood- Paley type, boundedness, Sobolev space, A priori estimates in context of PDEs, nondivergence form, Initial value problems for second-order parabolic equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, initial value problem, Stability in context of PDEs
Systems of elliptic equations, general, Cauchy problem, General theory of partial differential operators, a priori estimates, multilinear estimates of Littlewood- Paley type, boundedness, Sobolev space, A priori estimates in context of PDEs, nondivergence form, Initial value problems for second-order parabolic equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, initial value problem, Stability in context of PDEs
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