Turkish Journal of Mathematics
Abstract
Let $U\subseteq R^{n}$ (res. $D\subset R^{n}$) be an open (res. a compact) subset, and let $L$ be an elliptic operator defined on $C^{2}(U, R)$ (res. $C^{2}(D, R)$). In the present paper, we are going to extend the maximum principle for the function $f \in C^{2}(U, R)$ (res. $f \in C^{2}(D, R)$) satisfying the equation $Lf=\varepsilon$, where $\varepsilon$ is a real everywhere nonzero continuous function on $U$ (res. $D$). Finally, we obtain some applications in mathematics and physics.
DOI
10.3906/mat-1910-61
Keywords
Boundary behavior, elliptic operator, maximum principle, positive definite matrix
First Page
66
Last Page
80
Recommended Citation
PARSIAN, A (2021). An extension of maximum principle with some applications. Turkish Journal of Mathematics 45 (1): 66-80. https://doi.org/10.3906/mat-1910-61
