Solutions and eigenvalues of Laplace's equation on bounded open sets
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Date
2021-10-18
Authors
Yang, Guangchong
Lan, Kunquan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We obtain solutions for Laplace's and Poisson's equations on bounded open subsets of Rn, (n≥2), via Hammerstein integral operators involving kernels and Green's functions, respectively. The new solutions are different from the previous ones obtained by the well-known Newtonian potential kernel and the Newtonian potential operator. Our results on eigenvalue problems of Laplace's equation are different from the previous results that use the Newtonian potential operator and require n≥3. As a special case of the eigenvalue problems, we provide a result under an easily verifiable condition on the weight function when n≥3. This result cannot be obtained by using the Newtonian potential operator.
Description
Keywords
Eigenvalue, Laplace's equation, Poisson's equation, Green's function, Hammerstein integral operator
Citation
Yang, G., & Lan, K. (2021). Solutions and eigenvalues of Laplace's equation on bounded open sets. <i>Electronic Journal of Differential Equations, 2021</i>(87), pp. 1-15.