Isoperimetric estimates of the solutions of a class of pseudodifferential equations and their application to crack problems.

*(English. Russian original)*Zbl 0733.73055
J. Appl. Math. Mech. 53, No. 6, 831-835 (1989); translation from Prikl. Mat. Mekh. 53, No. 6, 1044-1048 (1989).

Summary: Isoperimetric estimates are obtained of solutions of boundary value problems for a class of pseudodifferential equations. This class of equations includes the equation of problems on plane normal discontinuity cracks located in a homogeneous linearly elastic space and an inhomogeneous space whose Young’s modulus has a power-law dependence on the distance to the plane of the crack. As it applies to crack problems, the established inequalities yield, in particular, isoperimetric estimates of the maximum opening of the crack and its volume under arbitrary loads.

##### MSC:

74R99 | Fracture and damage |

47G30 | Pseudodifferential operators |

52A40 | Inequalities and extremum problems involving convexity in convex geometry |

##### Keywords:

plane normal discontinuity cracks; homogeneous linearly elastic space; inhomogeneous space; isoperimetric estimates of the maximum opening; arbitrary loads
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\textit{E. I. Shifrin}, J. Appl. Math. Mech. 53, No. 6, 831--835 (1989; Zbl 0733.73055); translation from Prikl. Mat. Mekh. 53, No. 6, 1044--1048 (1989)

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##### References:

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