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- W2038615749 abstract "We extend the results of Part I [SIAM J. Appl. Math., 39 (1980), pp. 14–20] on the spectrum of the singular integral operator [ (A{bf M})(x) = - frac{1}{{4pi }}{operatorname{grad}}{operatorname{div}}int_Omega {frac{{{bf M}(y)}}{r}dy.} ] As an application we obtain an estimate of the lower bound of the spectrum of the magnetic field operator $R{bf M} = h{bf M} + A{bf M}$ from ${bf L}^2 Omega $ into the subspace J of generalized solenoidal vector-functions from ${bf L}^2 $. Here ${bf M}$ is the magnetization vector, $h{bf M} = ({{bf M} / {(mu (M,x) - 1)}})(M = | {bf M} |)$ is the total field, $A{bf M}$ is the induced field, and $Omega $ is a simply connected domain in $R_3 $." @default.
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- W2038615749 date "1981-07-01" @default.
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- W2038615749 title "Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. III" @default.
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- W2038615749 doi "https://doi.org/10.1137/0512046" @default.
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