Donatella Danielli
Publications
1.
A compact embedding
theorem for a class of degenerate Sobolev spaces.
Rendiconti Sem. Mat. Univ. Polit. Torino,
49(3); 399-420, 1991.
2.
Formules
de representation et theoremes
d’inclusion
pour des operateurs sous-elliptiques.
Comptes Rendus
Acad. Sci. Paris, t. 314, Serie I; 987-990, 1992.
3.
(with
L. Capogna and N. Garofalo) Embedding theorems and the Harnack inequality for solutions of nonlinear subelliptic equations. Comptes
Rendus Acad. Sci. Paris, t. 316, Serie I; 809-814, 1993.
4.
(with
L. Capogna and N. Garofalo) An embedding theorem
and the Harnack inequality for nonlinear subelliptic equations. Comm. in PDE, 18;
1765-1794, 1993.
5.
(with
L. Capogna and N. Garofalo)
Subelliptic
mollifiers and a characterization of Rellich and Poincaré domains. Rend Sem. Mat. Univ. Polit. Torino,
51(4); 361-386, 1993.
6.
(with
L. Capogna and N. Garofalo) An isoperimetric
inequality and the geometric Sobolev embedding for
vector fields. Mathematical Research Letters, 1; 263-268,
1994.
7.
(with
L. Capogna and N. Garofalo)
The geometric Sobolev embedding for vector fields and the
isoperimetric inequality. Comm. in Analysis and Geometry,
2(2); 203-215, 1994.
8.
Regularity at the
boundary for solutions of nonlinear subelliptic equations.
Indiana Univ. Math. J., 44(1); 269-286, 1995.
9.
(with
L. Capogna and N. Garofalo)
Capacitary
estimates and the local behavior of solutions of nonlinear subelliptic
equations. Amer. Jour. Mathematics, 118(6); 1153-1196, 1996.
10. (with L. Capogna
and N. Garofalo) Subelliptic
mollifiers and a basic pointwise estimate of Poincaré
type. Math. Zeitschrift, 226; 147-154,
1997.
11. (with N. Garofalo) Geometric properties
of solutions to subelliptic equations in nilpotent
Lie groups. Lecture Notes in Pure and Applied Mathematics,
vol.194, Reaction Diffusion Systems, Marcel Dekker Inc., 89-105,
1998.
12. (with N. Garofalo and D. M. Nhieu) Isoperimetric and trace
inequalities with respect to Carnot-Carathéodory
metrics. Geometry Seminars, 1996-97, Univ. of Bologna,
Bologna, 51-62, 1998.
13. (with N. Garofalo and D. M. Nhieu) Trace inequalities for
Carnot-Carathéodory spaces
and applications. Annali Scuola Normale Sup.
Pisa (4), 27; 195-252, 1998.
14. A Fefferman-Phong
type inequality and applications to quasilinear subelliptic
equations. Potential Analysis, 11 (4); 387-413, 1999.
15. (with N. Garofalo and
D. M. Nhieu) Sub-elliptic Besov spaces and the characterization of traces on lower
dimensional manifolds. Contemporary Mathematics, vol. 277,
Amer. Math. Soc., 19-37, 2001.
16. (with N. Garofalo) Properties of entire
solutions of non-uniformly elliptic equations arising in geometry and in phase
transitions. Calculus of Variations, 15 (4); 451-491, 2002.
17. (with N. Garofalo and S.
Salsa) Variational
inequalities with lack of ellipticity. Part I:
interior regularity and non-degeneracy of the free boundary, Indiana
Univ. Math. Jour., 52; 361-398, 2003.
18. (with A. Petrosyan
and H. Shahgholian) A singular perturbation
problem for the p-Laplace operator, Indiana Univ. Math. Jour., 52; 457-476, 2003.
19. (with N. Garofalo and D. M. Nhieu) On the best possible
character of the LQ norm in some a priori estimates for
non-divergence form equations in Carnot groups, Proc. Amer. Math. Soc.,
131; 3487-3498, 2003.
20. (with N. Garofalo and D. M. Nhieu) Notions of convexity in
Carnot groups, Comm. Anal. Geom., 11 (2); 263-341, 2003.
21. (with N. Garofalo, D. M. Nhieu, and F. Tournier) The Theorem of Busemann-Feller-Alexandrov in
Carnot Groups, Comm. Anal. Geom., 12 (4); 853-886, 2004.
22. (with A. Petrosyan)
A minimum problem
with free boundary for a degenerate quasilinear operator, Calculus of
Variations, 23 (1); 97-124, 2005.
23. (with M. Korten)
On the pointwise jump
condition of the free boundary in the 1-phase Stefan problem, Comm. Pure
Appl. Anal., 4 (2), 357-366, 2005.
24. (with N. Garofalo
and D. M. Nhieu) Non-doubling Ahlfors
measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory
spaces, Memoirs AMS.,
182 (857), 2006.
25. (with A. Petrosyan) Full regularity of the
free boundary in a Bernoulli-type problem in two dimensions, Math. Res. Lett., 13 (4),
667-681, 2006.
26. (with N. Garofalo and A. Petrosyan) The sub-elliptic obstacle
problem: C1,α regularity of
the free boundary in Carnot groups of step two, Adv. Math., 211,
485-516, 2007.
27. (with L. Capogna,
S. Pauls, and J. Tyson) An
Introduction to the Heisenberg Group and the sub-Riemannian Isoperimetric
Inequality, Progress in Mathematics, 259. Birkhäuser
Verlag, Basel, 2007.
28. (Editor) Recent Developments in Nonlinear
Partial Differential Equations, Contemporary Mathematics. Amer.
Math. Soc., 2007.
29. (with N. Garofalo and D. M. Nhieu) Sub-Riemannian
Calculus on Hypersurfaces in Carnot Groups, Adv. Math., 215 (1),
292-378, 2007.
30. (with N. Garofalo and D. M. Nhieu) A partial solution of the
isoperimetric problem for the Heisenberg group, Forum Mathematicum, 20(1), 99-143, 2008.
31. (with N. Garofalo and D. M. Nhieu) A notable family of
entire intrinsic minimal graphs in the Heisenberg group which are not
perimeter minimizing, Amer. Jour. Math., 130 (2), 317-339,
2008.
32. (with N. Garofalo)
Interior Cauchy-Schauder estimates for the heat flow in Carnot- Carathéodory spaces,
Methods Appl. Anal., 15 (1) (Special issue dedicated to N. Trudinger), 121-136, 2008.
33. (with N. Garofalo, D. M. Nhieu, and S. Pauls), Instability of graphical
strips and a positive answer to the Bernstein problem in the Heisenberg group,
Jour. Diff. Geom., 81 (2), 251-296, 2009.
34. (with N. Garofalo and P. C. Nguyen)
Inequalities of Hardy-Sobolev Type in Carnot- Carathéodory Spaces, Sobolev
Spaces in Mathematics I (V. Maz’ya ed.), International Mathematical Series,
Vol. 8, Springer, 117-152, 2009.
35. (with N. Garofalo and N. Marola) Local
behavior of p-harmonic
Green's functions in metric spaces, Potential Anal.,
32 (4), 343-362, 2010.
36. (with N. Garofalo and D. M. Nhieu) Sub-Riemannian
calculus and monotonicity of the perimeter for graphical strips, Math. Zeit., 265 (3),
617-637, 2010.
37. (with N. Garofalo, D. M. Nhieu, and S. Pauls) The Bernstein problem for embedded surfaces in the Heisenberg group , H1 Indiana Univ. Math. Jour., 59 (2), 563-594, 2010.
38. (with N. Garofalo and P.C. Nguyen) Sharp Hardy-Sobolev type inequalities in Carnot- Carathéodory
spaces. Potential
Analysis, 34 (3),
223-242, 2011.
39. (with
N. Garofalo and D.M. Nhieu)
Integrability of the sub-Riemannian mean curvature of surfaces
in the Heisenberg group. Proc.
AMS., 140,
811-821, 2012.
40. (with N. Garofalo, A. Petrosyan, and T. To) Optimal regularity and the free boundary in the parabolic Signorini problem. Memoirs AMS, 249 (1181), 103 p., 2017.
41. (with S. Salsa) Obstacle problems involving the fractional Laplacian. Recent Developments in the Nonlocal Theory (T. Kuusi and G. Palatucci, Eds.), Book Series on Measure Theory, De Gruyter, Berlin, 81-164, 2018.
42. (with
A. Petrosyan and C. Pop) Obstacle problems for nonlocal
operators. New developments in the
analysis of nonlocal operators, 191–214, Contemp.
Math., vol. 723, Amer. Math. Soc., 2019.