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Pointwise estimates of potentials for higher-order capacities

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Abstract

In a domain D=Ω\E∈ R n, we consider a nonlinear higher-order elliptic equation such that the corresponding energy space is W m p (D)⩜W 1 q (D), q>mp, and estimate a solution u(x) of this equation satisfying the condition u(x)−kf(x)∈W m p (D)⩜W 1 q (D), where k∈R 1, f(x)∈ C ∞0 (Ω), and f(x)=1 for x∈F. We establish a pointwise estimate for u(x) in terms of the higher-order capacity of the set F and the distance from the point x to the set F.

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References

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Authors
  1. I. V. Skrypnik
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Additional information

Academician. Ukrainian Academy of Sciences. Institute of Applied Mathematics and Mechanics, Donetsk. Translated from Ukrainskii Matematischeskii Zhurnal, Vol. 49, No. 1, pp. 149–163, January, 1997.

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Skrypnik, I.V. Pointwise estimates of potentials for higher-order capacities. Ukr Math J 49, 165–180 (1997). https://doi.org/10.1007/BF02486624

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  • DOI: https://doi.org/10.1007/BF02486624

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