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This article is cited in 8 scientific papers (total in 8 papers)
Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations
Yu. A. Dubinskii
Abstract:
The paper is devoted to the theory of “traces” in the spaces
$$
W^\infty\{a_\alpha,p_\alpha\}(G)=\biggl\{u(x)\in C^\infty(G):\quad\sum_{|\alpha|=0}^{\infty}a_\alpha\|D^\alpha u\|_{p_\alpha}^{p_\alpha}<\infty\biggr\}
$$
and to the inhomogeneous Dirichlet problem for elliptic equations of infinite order. A trace criterion is established, simple sufficient trace conditions are adduced, and the correctness of the indicated Dirichlet problem is proved on the basis of the results obtained.
Bibliography: 6 titles.
Received: 06.07.1977
Citation:
Yu. A. Dubinskii, “Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations”, Math. USSR-Sb., 34:5 (1978), 627–644
Linking options:
https://www.mathnet.ru/eng/sm2553https://doi.org/10.1070/SM1978v034n05ABEH001334 https://www.mathnet.ru/eng/sm/v148/i1/p66
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