Publications of Kevin R. Payne :
Journal
articles and refereed conference proceedings papers:
- Smooth tame Frechet
algebras and Lie groups of pseudodifferential
operators, Comm. Pure Appl. Math.
44 (1991), 309-337.
- Interior regularity of the Dirichlet problem for the Tricomi
equation, J. Math. Anal. Appl.
199 (1996), 271-292.
- Boundary geometry and location
of singularities for solutions to the Dirichlet
problem for Tricomi type equations, Houston J.Math. 23 (1997), 709-731.
- Propagation of singularities for
solutions to the Dirichlet problem for equations
of Tricomi type, Rend.
Sem. Mat. Univ. Politec.
Torino 54 (1996), 39-61.
- Solvability theorems for linear
equations of Tricomi type, J. Math. Anal. Appl. 215 (1997), 262-273.
- New facets of DFI, a DE solver
for all seasons,
(with F. R. Payne) in "Integral Methods in Science and Engineering,
Vol. 2 (Oulu
1996)'', 176-180, Pitman Res. Notes
Math. Ser. 375,
Longman, Harlow, 1997.
- Propagation of singularities
phenomena for equations of Tricomi type, Appl. Anal. 68 (1998), 195-206.
- A dual variational
approach to a class of nonlocal semilinear Tricomi problems (with D. Lupo),
NoDEA Nonlinear Differential Equations Appl. 6
(1999), 247-266.
- Existence of eigenvalues for reflected Tricomi
operators and applications to multiplicity of solutions for sublinear and asymptotically linear nonlocal Tricomi problems (with D. Lupo
and A. M. Micheletti), Adv. Differential Equations 4 (1999), 391-412.
- Linear and sublinear
Tricomi via DFI (with F. R. Payne), in ``Integral Methods
in Science and Engineering (Houghton, MI 1998)'', Chapman & Hall/CRC Res. Notes Math. 418, Chapman & Hall/CRC, Boca Raton, FL
2000.
- The dual variational method in nonlocal
semilinear Tricomi
problems (with D. Lupo), in ``Proceedings of
the Autumn School on Nonlinear Analysis and
Differential Equations'' , 321-338, Progr. Nonlinear Differential Equations Appl. 43,
Birkhauser Boston, Boston, MA
(2000).
- Multiplicity of nontrivial
solutions for an asymptotically linear nonlocal Tricomi problem (with D. Lupo), Nonlinear Anal. Ser. A: Theory Methods
46
(2001), 591-600.
- On the maximum
principle for generalized solutions to the Tricomi
problem (with D. Lupo), Commun. Contemp. Math. 2 (2000), 535-557.
- Existence of a principal eigenvalue for the Tricomi
problem (with
D. Lupo), Electron.
J. Differential Equations, Conf.
05 (2000), 173-180.
- Spectral bounds for Tricomi
problems and applications to semilinear
existence and existence with uniqueness (with D. Lupo),
J. Differential Equations 184
(2002), 139-162.
- Critical exponents for semilinear
equations of mixed elliptic-hyperbolic and degenerate types (with D. Lupo),
Comm. Pure. Appl. Math. 56 (2003), 403-424.
- Conservation laws for equations
of mixed elliptic-hyperbolic and degenerate types (with D. Lupo), Duke Math. J. 127 (2005), 251-290.
- Singular metrics and associated conformal groups for operators of
mixed and degenerate types, Ann. Mat. Pura Appl. 185 (2006),
613-625.
- Nonexistence of nontrivial solutions for supercritical equations of mixed
elliptic-hyperbolic type (with D. Lupo and N.I. Popivanov), 371-390, Progr. Nonlinear Differential Equations Appl.,
66, Birkhäuser Verlag,
Basel,
2006.
- On closed boundary value problems for equations of mixed
elliptic-hyperbolic type (with D. Lupo and C. S. Morawetz) Comm.
Pure Appl. Math., to appear.
- Weak well-posedness for the Dirichlet problem for equations of mixed
elliptic-hyperbolic type, Le Matematiche 60 (2005), 315-327.
- Multiplier methods for mixed type equations, Int. J. Appl. Math. Stat. 8 (2007), 58-75.
Preprints:
Theses:
- Smooth tame Frechet algebras and Lie groups of pseudodifferential
operators, Ph.D. Dissertation, SUNY-Stony Brook, 1989.