-Laplacian in does not lead to regularity

Author:
Nikan B. Firoozye

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

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Abstract: It is well known that in two space dimensions, if a solution to Poisson's equation has right-hand side in , then this solution is actually continuous. The corresponding result for *n*-Laplacians is shown to be false for ; we construct two examples with right-hand sides in 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

DOI:
https://doi.org/10.1090/S0002-9939-1995-1277110-0

Article copyright:
© Copyright 1995
American Mathematical Society