A Generalized Maximum Principle for Convolution Operators in Bounded Regions
Jörg Reißinger · Real Analysis Exchange · 2013
Dealing with the technically motivated concept of convolution operators in bounded regions of \\(\\mathbb{R}^{N}\\) with an underlying nearby boundary condition we extend a formerly proved result about the existence and uniqueness of suitable solutions for dimension \\(N\\leq 2\\) to arbitrary dimensions \\(N\\). Thus, a first substantial result in a sufficiently generalized form, beyond the very specific case of rectangular regions, is established in this field. The result can also be seen as a generalized maximum principle for so called \\(k\\)-harmonic functions where \\(k\\) is the kernel of the given convolution operator.