The main result of the present paper establishes a stability property of the first eigenvalue of the associated problem which deals with the $p(x)$-Laplacian on Riemannian manifolds with Dirichlet boundary condition.
Variable exponent Lebesgue and Sobolev spaces; first eigenvalue; Riemannian manifolds; $p(x)$-Laplacian.
MASHIYEV, R. A.; ALİSOY, GULİZAR; and OGRAS, SEZAİ
"Some properties of the first eigenvalue of the $p(x)$-laplacian on riemannian manifolds,"
Turkish Journal of Mathematics: Vol. 33:
4, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol33/iss4/5