Regularity properties of degenerate convolution-elliptic equations

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2016

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Springer

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The coercive properties of degenerate abstract convolution-elliptic equations are investigated. Here we find sufficient conditions that guarantee the separability of these problems in L-p spaces. It is established that the corresponding convolution-elliptic operator is positive and is also a generator of an analytic semigroup. Finally, these results are applied to obtain the maximal regularity properties of the Cauchy problem for a degenerate abstract parabolic equation in mixed L-p norms, boundary value problems for degenerate integro-differential equations, and infinite systems of degenerate elliptic integro-differential equations.

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positive operators, abstract weighted spaces, operator-valued multipliers, boundary value problems, convolution equations, integro-differential equations

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