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Removable sets for continuous solutions of semilinear elliptic equations

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Abstract

We discuss the possible removability of sets for continuous solutions of semilinear elliptic equations of the form −Δu = F(x, u). In particular, we show that a set E in \({\mathbb{R}^{n}}\) is removable for α-Hölder continuous solutions of such equations if and only if n − 2 + α-dimensional Hausdorff measure of E is zero.

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Authors and Affiliations

  1. Faculty of Education and Human Studies, Akita University, Akita, 010-8502, Japan

    Kentaro Hirata

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  1. Kentaro Hirata
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Correspondence to Kentaro Hirata.

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This work was partially supported by Grant-in-Aid for Young Scientists (B) (No. 22740081), Japan Society for the Promotion of Science.

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Hirata, K. Removable sets for continuous solutions of semilinear elliptic equations. manuscripta math. 135, 245–262 (2011). https://doi.org/10.1007/s00229-011-0440-2

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  • DOI: https://doi.org/10.1007/s00229-011-0440-2

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