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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$n$-Laplacian in $\mathcal {H}^ 1_ \mathrm {loc}$ does not lead to regularity
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by Nikan B. Firoozye PDF
Proc. Amer. Math. Soc. 123 (1995), 3357-3360 Request permission

Abstract:

It is well known that in two space dimensions, if a solution to Poisson’s equation has right-hand side in $\mathcal {H}_{{\text {loc}}}^1$, then this solution is actually continuous. The corresponding result for n-Laplacians is shown to be false for $n \geq 3$; we construct two examples with right-hand sides in $\mathcal {H}_{{\text {loc}}}^1({\Re ^n})$ such that the corresponding solutions to the n-Laplacian are unbounded in the first case, and bounded but discontinuous in the second.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 3357-3360
  • MSC: Primary 35J05; Secondary 42B30
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1277110-0
  • MathSciNet review: 1277110