Non-absolutely convergent generalized Laplacian (Q2067265)
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scientific article; zbMATH DE number 7458102
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-absolutely convergent generalized Laplacian |
scientific article; zbMATH DE number 7458102 |
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Non-absolutely convergent generalized Laplacian (English)
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18 January 2022
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The authors introduce a generalization of the Laplace operator, based on a new type of non-absolutely convergent integral. With this tool, the authors prove new Blaschke-Privaloff-type criteria for harmonicity and superharmonicity. Moreover, such integral, where the integrand may be a highly oscillating pointwise function or a distribution-valued function, provides a precise meaning to some generalized Poisson equations with general right hand side.
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generalization of the Laplace operator
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superharmonic functions
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harmonic functions
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