Referenze Bibliografiche
[ACMM]
A. ALVINO -
A. CIANCHI -
V. G. MAZ'YA -
A. MERCALDO,
Well-posed elliptic Neumann problems involving irregular data and domains,
Ann. Inst. H. Poincaré Anal. Non Linéaire,
27 (
2010), 1017-1054 |
fulltext (doi) |
MR 2659156 |
Zbl 1200.35105[Ba]
A. BAIDER,
Noncompact Riemannian manifolds with discrete spectra,
J. Diff. Geom. 14 (
1979), 41-57. |
MR 577877 |
Zbl 0411.58022[BGM]
M. BERGER -
P. GAUDUCHON -
E. MAZET,
Le spectre d'une variété Riemannienne,
Lecture notes in Mathematics 194,
Springer-Verlag, Berlin,
1971. |
MR 282313[BS]
M. S. BIRMAN -
M. Z. SOLOMJAK,
Spectral theory of self-adjoint operators in Hilbert space,
D. Reidel Publishing Company, Dordrecht,
1986. |
MR 1192782[Bou]
J. BOURGAIN,
Geodesic restrictions and $L^p$-estimates for eigenfunctions of Riemannian surfaces,
Amer. Math. Soc. Tranl. 226 (
2009), 27-25. |
fulltext (doi) |
MR 2500507 |
Zbl 1189.58015[BuZa]
YU. D. BURAGO -
V. A. ZALGALLER,
Geometric inequalities,
Springer-Verlag, Berlin,
1988. |
fulltext (doi) |
MR 936419[CF]
I. CHAVEL -
E. A. FELDMAN,
Modified isoperimetric constants, and large time heat diffusion in Riemannian manifolds,
Duke Math. J. 64 (
1991), 473-499. |
fulltext (doi) |
MR 1141283 |
Zbl 0753.58031[Che]
J. CHEEGER,
A lower bound for the smallest eigevalue of the Laplacian, in
Problems in analysis, 195-199,
Princeton Univ. Press, Princeton,
1970. |
MR 402831[Chi]
G. CHITI,
A reverse Hölder inequality for the eigenfunctions of linear second order elliptic operators,
Zeit. Angew. Math. Phys. (ZAMP)
33 (
1982), 143-148. |
fulltext (doi) |
MR 652928 |
Zbl 0508.35063[CGY]
F. CHUNG -
A. GRIGOR'YAN -
S.-T. YAU,
Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs,
Comm. Anal. Geom. 8 (
2000), 969-1026. |
fulltext (doi) |
MR 1846124 |
Zbl 1001.58022[Ci1]
A. CIANCHI,
On relative isoperimetric inequalities in the plane,
Boll. Un. Mat. Ital. 3-B (
1989), 289-326. |
MR 997998 |
Zbl 0674.49030[Ci3]
A. CIANCHI,
Moser-Trudinger inequalities without boundary conditions and isoperimetric problems,
Indiana Univ. Math. J. 54 (
2005), 669-705. |
fulltext (doi) |
MR 2151230 |
Zbl 1097.46016[CM2]
A. CIANCHI -
V. G. MAZ'YA,
On the discreteness of the spectrum of the Laplacian on complete Riemannian manifolds,
J. Diff. Geom. 87 (
2011), 469-491. |
MR 2819545[CM3]
A. CIANCHI -
V. G. MAZ'YA,
Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds,
Amer. J. Math., to appear. |
fulltext (doi) |
MR 3068397[CM4]
A. CIANCHI -
V. G. MAZ'YA,
Boundedness of solutions to the Schrödinger equation under Neumann boundary conditions,
J. Math. Pures Appl. 98 (
2012), 654-688. |
fulltext (doi) |
MR 2994697[CH]
R. COURANT -
D. HILBERT,
Methoden der mathematischen Physik,
Springer, Berlin,
1937. |
MR 344038 |
Zbl 63.0449.05[D]
E. DE GIORGI,
Sulla proprietà isoperimetrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita, (Italian)
Atti Accad. Naz. Lincei. Mem. Cl. Sci. Fis. Mat. Nat. Sez. I
5 (
1958) 33-44. |
MR 98331 |
Zbl 0116.07901[DL]
H. DONNELLY -
P. LI,
Pure point spectrum and negative curvature for noncompact manifolds,
Duke Math. J. 46 (
1979), 497-503. |
MR 544241 |
Zbl 0416.58025[Ga]
S. GALLOT,
Inégalités isopérimétriques et analitiques sur les variétés riemanniennes,
Asterisque 163 (
1988), 31-91. |
MR 999971[Gr1] A. GRIGOR'YAN, On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds, Mat. Sbornik 128 (1985), 354-363 (Russian); English translation: Math. USSR Sb. 56 (1987), 349-358.
[Gr2]
A. GRIGOR'YAN,
Isoperimetric inequalities and capacities on Riemannian manifolds, in
The Maz'ya anniversary collection, Vol. 1 (Rostock, 1998), 139-153,
Oper. Theory Adv. Appl.,
109,
Birkhuser, Basel,
1999. |
MR 1747869[HK]
P. HAIASZ -
P. KOSKELA,
Isoperimetric inequalites and imbedding theorems in irregular domains,
J. London Math. Soc. 58 (
1998), 425-450. |
fulltext (doi) |
MR 1668136[He]
E. HEBEY,
Nonlinear analysis on manifolds: Sobolev spaces and inequalities,
American Math. Soc., Providence,
1999. |
MR 1688256 |
Zbl 0981.58006[HSS]
R. HEMPEL -
L. SECO -
B. SIMON,
The essential spectrum of Neumann Laplacians on some bounded singular domains,
J. Funct. Anal. 102 (
1991), 448-483. |
fulltext (doi) |
MR 1140635 |
Zbl 0741.35043[HHN]
M. HOFFMANN-OSTENHOF -
T. HOFFMANN-OSTENHOF -
N. NADIRASHVILI,
On the multiplicity of eigenvalues of the Laplacian on surfaces,
Ann. Global Anal. Geom. 17 (
1999), 43-48. |
fulltext (doi) |
MR 1674331 |
Zbl 0923.35109[JMS]
V. JAKSIC -
S. MOLCHANOV -
B. SIMON,
Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps,
J. Funct. Anal. 106 (
1992), 59-79. |
fulltext (doi) |
MR 1163464 |
Zbl 0783.35040[La]
D. A. LABUTIN,
Embedding of Sobolev spaces on Hölder domains,
Proc. Steklov Inst. Math. 227 (
1999), 163-172 (Russian); English translation:
Trudy Mat. Inst. 227 (
1999), 170-179. |
MR 1784315[MZ]
J. MALYÂ -
W. P. ZIEMER,
Fine regularity of solutions of elliptic partial differential equations,
American Mathematical Society, Providence,
1997. |
fulltext (doi) |
MR 1461542[Ma1]
V. G. MAZ'YA,
Classes of regions and imbedding theorems for function spaces,
Dokl. Akad. Nauk. SSSR 133 (
1960), 527-530 (Russian); English translation:
Soviet Math. Dokl. 1 (
1960), 882-885. |
MR 126152[Ma2]
V. G. MAZ'YA,
Some estimates of solutions of second-order elliptic equations,
Dokl. Akad. Nauk. SSSR 137 (
1961), 1057-1059 (Russian); English translation:
Soviet Math. Dokl. 2 (
1961), 413-415. |
MR 131054[Ma3]
V. G. MAZ'YA,
On p-conductivity and theorems on embedding certain functional spaces into a C-space,
Dokl. Akad. Nauk SSSR,
140 (
1961), 299-302 (Russian). |
MR 157224[Ma4]
V. G. MAZ'YA,
On the solvability of the Neumann problem,
Dokl. Akad. Nauk SSSR,
147 (
1962), 294-296 (Russian). |
MR 144058[Ma5]
V. G. MAZ'YA,
The Neumann problem in regions with nonregular boundaries,
Sibirsk. Mat. Ž. 9 (
1968), 1322-1350 (Russian). |
MR 239270[Ma6]
V. G. MAZ'YA,
On weak solutions of the Dirichlet and Neumann problems,
Trusdy Moskov. Mat. Obšč. 20 (
1969), 137-172 (Russian); English translation:
Trans. Moscow Math. Soc. 20 (
1969), 135-172 |
MR 259329[Ma7]
V. G. MAZ'YA,
Sobolev spaces with applications to elliptic partial differential equations,
Springer, Heidelberg,
2011. |
fulltext (doi) |
MR 2777530[MHH]
F. MORGAN -
H. HOWARDS -
M. HUTCHINGS,
The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature,
Trans. Amer. Math. Soc,
352 (
2000), 4889-4909. |
fulltext (doi) |
MR 1661278 |
Zbl 0976.53082[Na]
N. NADIRASHVILI,
Isoperimetric inequality for the second eigenvalue of a sphere,
J. Diff. Geom. 61 (
2002), 335-340. |
MR 1972149 |
Zbl 1071.58024[PR]
L. E. PAYNE -
M. E. RAYNER,
An isoperimetric inequality for the first eigenfunction in the fixed membrane problem,
Z. Angew. Math. Phys. 23 (
1972), 13-15. |
fulltext (doi) |
MR 313649 |
Zbl 0241.73080[Pi]
CH. PITTET,
The isoperimetric profile of homogeneous Riemannian manifolds,
J. Diff. Geom. 54 (
2000), 255-302. |
MR 1818180 |
Zbl 1035.53069[RS] M. REED - B. SIMON, Analysis of Operators IV, Academic Press, New York, 1972.
[Ri]
M. RITORÉ ,
Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces,
Comm. Anal. Geom. 9 (
2001), 1093-1138. |
fulltext (doi) |
MR 1883725 |
Zbl 1018.53003[Ro] W. RÖLKE, Uber den Laplace-Operator auf Riemannschen Mannigfaltigkeiten mit diskontinuierlichen Gruppen, Math. Nachr. 21 (1960), 132-149.
[Sa]
L. SALOFF-COSTE,
Sobolev inequalities in familiar and unfamiliar settings, in
Sobolev spaces in mathematics, Vol I, Sobolev type inequalities,
V.G. Maz'ya editor,
Springer,
2009. |
fulltext (doi) |
MR 2508847 |
Zbl 1165.26011[So]
C. D. SOGGE,
Lectures on eigenfunctions of the Laplacian,
Topics in mathematical analysis, 337-360,
Ser. Anal. Appl. Comput.,
3,
World Sci. Publ., Hackensack, NJ,
2008. |
fulltext (doi) |
MR 2462960 |
Zbl 1170.35071