What question did this study set out to answer?

To establish sufficient conditions under which an improved Hardy-type inequality with weight and potential terms holds on Riemannian manifolds.

August 21, 2023Complex Variables and Elliptic EquationsOpen Access

Improved Hardy inequalities on Riemannian manifolds

View Full Paper

Ask AI

Bookmark

Authors

KMKaushik MohantaCharles University JTJagmohan TyagiIndian Institute of Technology Gandhinagar

Discussion

Member takes

Implication

Mathematical analysis demonstrates improved Hardy-type inequalities on Riemannian manifolds, indicating generalized functional bounds across curved geometric domains.

Key Points

To establish sufficient conditions under which an improved Hardy-type inequality with weight and potential terms holds on Riemannian manifolds.
Analyzed integral inequalities for smooth, compactly supported test functions on arbitrary domains within a Riemannian manifold (M, g).
Derived analytical criteria constraining exponent p, weight parameters alpha and beta, function rho, and potential term V.
Formulated a generalized Hardy inequality incorporating an explicit potential term and variable weights on curved manifolds.
Demonstrated that the derived functional setup generalizes established Hardy inequalities, encompassing Euclidean space and broader geometric settings.

Cite This Study

Mohanta et al. (2023) studied this question.

synapsesocial.com/papers/69e5c8b862acec12c37f89f3 https://doi.org/10.1080/17476933.2023.2247998

View Full Paper

Ask AI

Bookmark

Implication

Mathematical analysis demonstrates improved Hardy-type inequalities on Riemannian manifolds, indicating generalized functional bounds across curved geometric domains.

Improved Hardy inequalities on Riemannian manifolds

Discussion

Member takes

Implication

Key Points

Cite This Study

Improved Hardy inequalities on Riemannian manifolds

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider