Decomposition of the spaces \(W_p^m\) and \(D_p^{m,k}\) into sums of solenoidal and potential subspaces and factorization inequalities

DOI10.1134/S1064562406030094zbMath1327.46035MaRDI QIDQ492370

Yulii A. Dubinskii

Publication date: 20 August 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Normally resolvable operators and direct decompositions of Sobolev spaces ⋮ Decompositions of the Sobolev-Clifford modules and nonlinear variational problems ⋮ Bilateral scales of Hardy inequalities and their applications to some problems of mathematical physics ⋮ Irrotational and solenoidal fields in the spaces \(W_p^m\)