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- W4256204012 abstract "A generalization of the classical energy inequality is obtained for evolution operators $(partial /partial t)I - H(t){Lambda ^{2k}} - J(t)$, associated with higher order linear parabolic operators with variable coefficients. Here $H(t)$ and $J(t)$ are matrices of singular integral operators. The key to the result is an algebraic inequality involving matrices similar to the symbol of $H(t)$ having their eigenvalues contained in a fixed compact subset of the open left-half complex plane. Then a sharp estimate on the norms of certain imbedding maps is obtained. These estimates along with the energy inequality is applied to the Cauchy problem for higher order linear parabolic operators restricted to slabs in ${R^{n + 1}}$." @default.
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- W4256204012 date "1972-03-01" @default.
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- W4256204012 title "An Energy Inequality for Higher Order Linear Parabolic Operators and Its Applications" @default.
- W4256204012 doi "https://doi.org/10.2307/1995881" @default.
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