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Chapter 3. High-order elliptic equations
[chapter]

1997
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Spherical Means for PDEs
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In this section we give a general scheme of construction of the spherical mean value relations for high-order elliptic equations (see [37] and [38]). Let X be a locally compact Hausdorf space, and let CQ(X) be a space of continuous functions / : X -* H with a compact support. We denote by R(X) the space of Radon measures FI : CQ{X) -• JR. Let B(xo, r) be a ball, and let IIjB(xo, r) be the balayage operator for the problem Lu -0 in the ball B(xo, r ) C G where r is sufficiently small. Let cr£o

doi:10.1515/9783110926026-004
fatcat:puarwlowlvcvvmddc6a6ahtnhe