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Coercive estimates for a class of differential operators

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Abstract

A description is given of all matrix differential operators of the form d/dt + tkA, satisfying in L2(Rn) the coercive estimate\(\left\| {\frac{d}{{dt}}u} \right\| \le c\left\| {B\frac{d}{{dt}}u + t^k Au} \right\|\) and the estimate

$$\left\| u \right\| \le c\left\| {B\frac{d}{{dt}}u + t^k Au} \right\|.$$

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Literature cited

  1. L. Hörmander, Pseudodifferential Operators and Nonelliptic Boundary-Value Problems [Russian translation], Mir, Moscow (1967), pp. 166–296.

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  2. Yu. V. Egorov, “Pseudodifferential operators of principal type,” Mat. Sb.,73, No. 3, 356–373 (1967).

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Authors and Affiliations

  1. All-Union Correspondence Institute of Mechanical Engineering, USSR

    B. P. Paneyakh

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  1. B. P. Paneyakh
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Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 725–732, November, 1976.

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Paneyakh, B.P. Coercive estimates for a class of differential operators. Mathematical Notes of the Academy of Sciences of the USSR 20, 965–969 (1976). https://doi.org/10.1007/BF01146920

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  • DOI: https://doi.org/10.1007/BF01146920

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