Araújo Filho, Marcio C.; Gomes, José N. V. Eigenvalue estimates for a class of elliptic differential operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space. (English) Zbl 1520.58012 Z. Angew. Math. Phys. 74, No. 4, Paper No. 157, 16 p. (2023). MSC: 58J50 47A75 47F10 35P15 53C25 PDFBibTeX XMLCite \textit{M. C. Araújo Filho} and \textit{J. N. V. Gomes}, Z. Angew. Math. Phys. 74, No. 4, Paper No. 157, 16 p. (2023; Zbl 1520.58012) Full Text: DOI arXiv
Araújo Filho, Marcio C.; Gomes, José N. V. Estimates of eigenvalues of an elliptic differential system in divergence form. (English) Zbl 07595886 Z. Angew. Math. Phys. 73, No. 5, Paper No. 210, 25 p. (2022). MSC: 47A75 47F05 35P15 53C24 53C25 PDFBibTeX XMLCite \textit{M. C. Araújo Filho} and \textit{J. N. V. Gomes}, Z. Angew. Math. Phys. 73, No. 5, Paper No. 210, 25 p. (2022; Zbl 07595886) Full Text: DOI arXiv
Araújo Filho, Marcio C. Inequalities for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds. (English) Zbl 1485.35302 Z. Angew. Math. Phys. 73, No. 2, Paper No. 47, 28 p. (2022). MSC: 35P15 35J25 47A75 53C42 53C25 PDFBibTeX XMLCite \textit{M. C. Araújo Filho}, Z. Angew. Math. Phys. 73, No. 2, Paper No. 47, 28 p. (2022; Zbl 1485.35302) Full Text: DOI arXiv
Roth, Julien; Upadhyay, Abhitosh Anisotropic eigenvalues upper bounds for hypersurfaces in weighted Euclidean spaces. (English) Zbl 1462.53004 Differ. Geom. Appl. 74, Article ID 101696, 14 p. (2021). MSC: 53A07 53C21 58J50 PDFBibTeX XMLCite \textit{J. Roth} and \textit{A. Upadhyay}, Differ. Geom. Appl. 74, Article ID 101696, 14 p. (2021; Zbl 1462.53004) Full Text: DOI
Lamboley, Jimmy; Sicbaldi, Pieralberto Existence and regularity of Faber-Krahn minimizers in a Riemannian manifold. (English. French summary) Zbl 1445.35266 J. Math. Pures Appl. (9) 141, 137-183 (2020). MSC: 35P15 58J05 35R35 49Q10 49R05 53C21 74P20 PDFBibTeX XMLCite \textit{J. Lamboley} and \textit{P. Sicbaldi}, J. Math. Pures Appl. (9) 141, 137--183 (2020; Zbl 1445.35266) Full Text: DOI arXiv
Tacy, Melissa \(L^p\) estimates for joint quasimodes of semiclassical pseudodifferential operators. (English) Zbl 1418.35287 Isr. J. Math. 232, No. 1, 401-425 (2019). Reviewer: Dumitru Motreanu (Perpignan) MSC: 35P15 35J15 53C21 PDFBibTeX XMLCite \textit{M. Tacy}, Isr. J. Math. 232, No. 1, 401--425 (2019; Zbl 1418.35287) Full Text: DOI arXiv
Galkowski, Jeffrey The \(L^{2}\) behavior of eigenfunctions near the glancing set. (English) Zbl 1362.53046 Commun. Partial Differ. Equations 41, No. 10, 1619-1648 (2016). MSC: 53C21 35P20 58J40 35J15 PDFBibTeX XMLCite \textit{J. Galkowski}, Commun. Partial Differ. Equations 41, No. 10, 1619--1648 (2016; Zbl 1362.53046) Full Text: DOI arXiv
Zhu, Yuming; Liu, Gusheng; Du, Feng Eigenvalue inequalities of elliptic operators in weighted divergence form on smooth metric measure spaces. (English) Zbl 1342.35194 J. Inequal. Appl. 2016, Paper No. 191, 15 p. (2016). MSC: 35P15 53C20 53C42 PDFBibTeX XMLCite \textit{Y. Zhu} et al., J. Inequal. Appl. 2016, Paper No. 191, 15 p. (2016; Zbl 1342.35194) Full Text: DOI
Chang, Sun-Yung Alice (ed.); De Lellis, Camillo (ed.); Topping, Peter (ed.) Partial differential equations. Abstracts from the workshop held August 2–8, 2015. (English) Zbl 1380.00050 Oberwolfach Rep. 12, No. 3, 2065-2124 (2015). MSC: 00B05 00B25 35J25 35J35 35J60 58J05 35K55 35P15 49N60 49R05 49Q05 49Q15 49Q20 53A30 53C44 53C45 35-06 49-06 53-06 PDFBibTeX XMLCite \textit{S.-Y. A. Chang} (ed.) et al., Oberwolfach Rep. 12, No. 3, 2065--2124 (2015; Zbl 1380.00050) Full Text: DOI
Stepanov, Sergey E.; Mikeš, Josef The spectral theory of the Yano rough Laplacian with some of its applications. (English) Zbl 1317.53058 Ann. Global Anal. Geom. 48, No. 1, 37-46 (2015). MSC: 53C21 53C24 58J40 58A14 PDFBibTeX XMLCite \textit{S. E. Stepanov} and \textit{J. Mikeš}, Ann. Global Anal. Geom. 48, No. 1, 37--46 (2015; Zbl 1317.53058) Full Text: DOI
Stepanov, S. E.; Mikeš, J. The Hodge-de Rham Laplacian and Tachibana operator on a compact Riemannian manifold with curvature operator of definite sign. (English. Russian original) Zbl 1320.53040 Izv. Math. 79, No. 2, 375-387 (2015); translation from Izv. Ross. Akad. Nauk, Ser. Mat 79, No. 2, 167-180 (2015). Reviewer: Peter B. Gilkey (Eugene) MSC: 53C20 58A10 58J60 35P15 PDFBibTeX XMLCite \textit{S. E. Stepanov} and \textit{J. Mikeš}, Izv. Math. 79, No. 2, 375--387 (2015; Zbl 1320.53040); translation from Izv. Ross. Akad. Nauk, Ser. Mat 79, No. 2, 167--180 (2015) Full Text: DOI
Stepanov, Sergey E.; Mikeš, Josef Eigenvalues of the Tachibana operator which acts on differential forms. (English) Zbl 1327.53046 Differ. Geom. Appl. 35, Suppl., 19-25 (2014). MSC: 53C21 53C20 53C24 PDFBibTeX XMLCite \textit{S. E. Stepanov} and \textit{J. Mikeš}, Differ. Geom. Appl. 35, 19--25 (2014; Zbl 1327.53046) Full Text: DOI arXiv
Canzani, Yaiza On the multiplicity of eigenvalues of conformally covariant operators. (Sur la multiplicité des valeurs propres d’opérateurs covariants conformes.) (English. French summary) Zbl 1320.53042 Ann. Inst. Fourier 64, No. 3, 947-970 (2014). Reviewer: Jesus Muciño-Raymundo (Morelia) MSC: 53C21 58J05 58J50 PDFBibTeX XMLCite \textit{Y. Canzani}, Ann. Inst. Fourier 64, No. 3, 947--970 (2014; Zbl 1320.53042) Full Text: DOI arXiv
Du, Feng; Wu, Chuanxi; Li, Guanghan; Xia, Changyu Eigenvalues of the buckling problem of arbitrary order and of the polyharmonic operator on Ricci flat manifolds. (English) Zbl 1327.35270 J. Math. Anal. Appl. 417, No. 2, 601-621 (2014). Reviewer: Andrew Bucki (Edmond) MSC: 35P15 35J40 53C20 58J32 47A75 PDFBibTeX XMLCite \textit{F. Du} et al., J. Math. Anal. Appl. 417, No. 2, 601--621 (2014; Zbl 1327.35270) Full Text: DOI
Sogge, Christopher D. Hangzhou lectures on eigenfunctions of the Laplacian. (English) Zbl 1312.58001 Annals of Mathematics Studies 188. Princeton, NJ: Princeton University Press (ISBN 978-0-691-16078-8/pbk; 978-0-691-16075-7/hbk; 978-1-400-85054-9/ebook). x, 193 p. (2014). Reviewer: Massimo Lanza de Cristoforis (Padova) MSC: 58-02 35-02 35J05 35P10 35S05 37A05 53C21 58J05 58J50 PDFBibTeX XMLCite \textit{C. D. Sogge}, Hangzhou lectures on eigenfunctions of the Laplacian. Princeton, NJ: Princeton University Press (2014; Zbl 1312.58001) Full Text: DOI Link
Dalbono, Francesca; Portaluri, Alessandro Morse-Smale index theorems for elliptic boundary deformation problems. (English) Zbl 1245.35020 J. Differ. Equations 253, No. 2, 463-480 (2012). MSC: 35J25 53D12 47A53 35P15 PDFBibTeX XMLCite \textit{F. Dalbono} and \textit{A. Portaluri}, J. Differ. Equations 253, No. 2, 463--480 (2012; Zbl 1245.35020) Full Text: DOI
Jost, Jürgen; Li-Jost, Xianqing; Wang, Qiaoling; Xia, Changyu Universal bounds for eigenvalues of the polyharmonic operators. (English) Zbl 1222.35132 Trans. Am. Math. Soc. 363, No. 4, 1821-1854 (2011). Reviewer: Agostino Prástaro (Roma) MSC: 35P15 53C20 35J30 58J05 PDFBibTeX XMLCite \textit{J. Jost} et al., Trans. Am. Math. Soc. 363, No. 4, 1821--1854 (2011; Zbl 1222.35132) Full Text: DOI arXiv
Grosjean, Jean-Francois; Humbert, Emmanuel The first eigenvalue of Dirac and Laplace operators on surfaces. arXiv:math/0609493 Preprint, arXiv:math/0609493 [math.DG] (2006). MSC: 34L15 53C27 58J05 BibTeX Cite \textit{J.-F. Grosjean} and \textit{E. Humbert}, ``The first eigenvalue of Dirac and Laplace operators on surfaces'', Preprint, arXiv:math/0609493 [math.DG] (2006) Full Text: arXiv
Véron, Laurent Première valeur propre non nulle du \(p\)-laplacien et équations quasi linéaires elliptiques sur une variété riemannienne compacte. (First nonzero eigenvalue of the \(p\)-Laplacian and quasilinear elliptic equations on a compact Riemannian manifold). (French. Abridged English version) Zbl 0782.58051 C. R. Acad. Sci., Paris, Sér. I 314, No. 4, 271-276 (1992). Reviewer: N.J.Hitchin (Coventry) MSC: 58J50 58J05 53C20 49R50 PDFBibTeX XMLCite \textit{L. Véron}, C. R. Acad. Sci., Paris, Sér. I 314, No. 4, 271--276 (1992; Zbl 0782.58051)
Müller, Werner Eigenvalue estimates for locally symmetric spaces of finite volume. (English) Zbl 0693.58033 Partial differential equations, Proc. Symp., Holzhau/GDR 1988, Teubner- Texte Math. 112, 179-196 (1989). Reviewer: J.Marschall MSC: 58J50 53C35 PDFBibTeX XML
Atiyah, Michael Eigenvalues of the Dirac operator. (English) Zbl 0568.53022 Arbeitstag. Bonn 1984, Proc. Meet. Max-Planck-Inst. Math., Bonn 1984, Lect. Notes Math. 1111, 251-260 (1985). Reviewer: P.Cherrier MSC: 53C20 58J99 35J99 PDFBibTeX XML
Guillemin, Victor A new proof of Weyl’s formula on the asymptotic distribution of eigenvalues. (English) Zbl 0559.58025 Adv. Math. 55, 131-160 (1985). Reviewer: N.Jacob MSC: 58J50 81S99 35P20 58J40 53D50 PDFBibTeX XMLCite \textit{V. Guillemin}, Adv. Math. 55, 131--160 (1985; Zbl 0559.58025) Full Text: DOI
Bando, Shigetoshi; Urakawa, Hajime Generic properties of the eigenvalue of the Laplacian for compact Riemannian manifolds. (English) Zbl 0534.58038 Tôhoku Math. J., II. Ser. 35, 155-172 (1983). Reviewer: D.Perrone MSC: 58J60 58J50 53C20 PDFBibTeX XMLCite \textit{S. Bando} and \textit{H. Urakawa}, Tôhoku Math. J. (2) 35, 155--172 (1983; Zbl 0534.58038) Full Text: DOI
Brüning, Jochen; Heintze, Ernst Representations of compact Lie groups and elliptic operators. (English) Zbl 0392.58015 Invent. Math. 50, 169-203 (1979). MSC: 58J50 22C05 53C20 53C10 35P20 58J10 58J32 PDFBibTeX XMLCite \textit{J. Brüning} and \textit{E. Heintze}, Invent. Math. 50, 169--203 (1979; Zbl 0392.58015) Full Text: DOI EuDML
Guillemin, Victor Lectures on spectral theory of elliptic operators. (English) Zbl 0447.58033 Duke Math. J. 44, 485-517 (1977). MSC: 58J50 58J10 53D50 70H99 58J40 37G99 22E46 43A80 PDFBibTeX XMLCite \textit{V. Guillemin}, Duke Math. J. 44, 485--517 (1977; Zbl 0447.58033) Full Text: DOI