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.