Mean Value Properties of Solutions to the Helmholtz and Modified Helmholtz Equations

Author:

Kuznetsov N.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Mathematics,Statistics and Probability

Reference21 articles.

1. H. Weber, “Ueber einige bestimmte Integrale” [in German], J. Reine Angew. Math. 69, 222–237 (1868).

2. H. Weber, “Ueber die Integration der partiellen Differentialgleichung: $$ \frac{\partial^2u}{\partial {x}^2}+\frac{\partial^2u}{\partial {y}^2}+{k}^2u=0 $$”[In German] Math. Ann. 1, 1–36 (1869).

3. R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II: Partial Differential Equations, John Wiley and Sons, New York etc. (1962).

4. P. Pizzetti, “Sul significato geometrico del secondo parametro differenziale di nLnia ftnnzione sopra una superficie qualunque” [in Italian], Rom. Acc. L. Rend. (5) 18, 309–316 (1909).

5. N. Kuznetsov, “Metaharmonic functions: mean flux theorem, its converse and related properties,” Algebra Anal. [in Russian] 33, No. 2, 82–97 (2021).

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