본문 바로가기
KERD
논문KCI 등재

SOME INTEGRAL INEQUALITIES FOR THE LAPLACIAN WITH DENSITY ON WEIGHTED MANIFOLDS WITH BOUNDARY

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

In this paper, we derive a Reilly-type inequality for the Laplacian with density on weighted manifolds with boundary. As its applications, we obtain some new Poincar\'{e}-type inequalities not only on weighted manifolds, but more interestingly, also on their boundary. Furthermore, some mean-curvature type inequalities on the boundary are also given.

Abstract

In this paper, we derive a Reilly-type inequality for the Laplacian with density on weighted manifolds with boundary. As its applications, we obtain some new Poincar\'{e}-type inequalities not only on weighted manifolds, but more interestingly, also on their boundary. Furthermore, some mean-curvature type inequalities on the boundary are also given.

참고문헌 (19)

  1. D. Bakry, "Diffusions hypercontractives", Lecture Notes in Mathematics, pp.177~206 (1985), Springer Berlin Heidelberg[DOI]
  2. F. Du, "Estimates for eigenvalues of weighted Laplacian and weighted p-Laplacian", Hiroshima Math. J, 51(3), pp.335~353 (2021)[DOI]
  3. A.G.C. Freitas, "Some Almost-Schur type inequalities for k−Bakry-Emery Ricci tensor", Differential Geometry and its Applications, 66, pp.82~92 (2019), Elsevier BV[DOI]
  4. Guangyue Huang, "Liouville type theorems of a nonlinear elliptic equation for the V-Laplacian", Analysis and Mathematical Physics, 8(1), pp.123~134 (2017), Springer Science and Business Media LLC[DOI]
  5. Guangyue HUANG, "Sharp bounds for the first nonzero Steklov eigenvalues for$f$-Laplacians", TURKISH JOURNAL OF MATHEMATICS, 40, pp.770~783 (2016), The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM) - DIGITAL COMMONS JOURNALS[DOI]
  6. GUANGYUE HUANG, "Eigenvalue estimates for submanifolds with bounded f-mean curvature", Proceedings - Mathematical Sciences, 127(2), pp.375~381 (2016), Springer Science and Business Media LLC[DOI]
  7. Qin Huang, "Applications of some elliptic equations in Riemannian manifolds", Journal of Mathematical Analysis and Applications, 409(1), pp.189~196 (2014), Elsevier BV[DOI]
  8. Alexander V. Kolesnikov, "Brascamp–Lieb-Type Inequalities on Weighted Riemannian Manifolds with Boundary", The Journal of Geometric Analysis, 27(2), pp.1680~1702 (2016), Springer Science and Business Media LLC[DOI]
  9. Alexander V. Kolesnikov, "Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds", American Journal of Mathematics, 140(5), pp.1147~1185 (2018), Project MUSE[DOI]
  10. Xiang-Dong Li, "Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds", Journal de Mathématiques Pures et Appliquées, 84(10), pp.1295~1361 (2005), Elsevier BV[DOI]
  11. H. Li, "f-minimal surface and manifold with positive m-Bakry-Emery Ricci curvature", J. Geom. Anal, 25(1), pp.421~435 (2015)[DOI]
  12. Li Ma, "Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians", Comptes Rendus. Mathématique, 348(21-22), pp.1203~1206 (2010), Cellule MathDoc[DOI]
  13. Aïssatou Mossèle Ndiaye, "About Bounds for Eigenvalues of the Laplacian with Density", Symmetry, Integrability and Geometry: Methods and Applications (2020), SIGMA (Symmetry, Integrability and Geometry: Methods and Application)[DOI]
  14. Robert Reilly, "Applications of the Hessian operator in a Riemannian manifold", Indiana University Mathematics Journal, 26(3), pp.459~ (1977), Indiana University Mathematics Journal[DOI]
  15. Qiang Tu, "Boundary effect of m-dimensional Bakry-Émery Ricci curvature", Analysis and Mathematical Physics, 9(3), pp.1319~1331 (2018), Springer Science and Business Media LLC[DOI]
  16. Guofang Wei, "Comparison geometry for the Bakry-Emery Ricci tensor", Journal of Differential Geometry, 83(2) (2009), International Press of Boston[DOI]
  17. Fanqi Zeng, "Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian", 대한수학회보, 56(4), pp.853~865 (2019), 대한수학회[DOI]
  18. Fanqi Zeng, "Gradient Estimates for a Nonlinear Parabolic Equation on Complete Smooth Metric Measure Spaces", Mediterranean Journal of Mathematics, 18(4) (2021), Springer Science and Business Media LLC[DOI]
  19. Yecheng Zhu, "Some integral inequalities for L operator and their applications on self-shrinkers", Journal of Mathematical Analysis and Applications, 463(2), pp.645~658 (2018), Elsevier BV[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (19건)