Nonlinear degenerate parabolic equations with singular coefficients for Greiner vector fields

References

• Goldstein , GR , Goldstein , JA and Kombe , I . 2005 . Nonlinear parabolic equations with singular coefficient and critical exponent . Appl. Anal. , 84 : 571 – 583 .
   Google Scholar
• Kalashnikov , AS . 1987 . Some problems of the qualitative theory of nonlinear degenerate second order parabolic equations . Russian Math. Surveys , 42 : 169 – 222 .
   Web of Science ®Google Scholar
• Diaz , JI and Thelin , F . 1994 . On a nonlinear parabolic problem arising in some models related to turbulent flows . SIAM J. Math. Anal. , 25 : 1085 – 1111 .
   Web of Science ®Google Scholar
• Baras , P and Goldstein , JA . 1984 . The heat equation with a singular potential . Trans. Amer. Math. Soc. , 284 : 121 – 139 .
   Web of Science ®Google Scholar
• Cabré , X and Martel , Y . 1999 . Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier . C.R. Acad. Sci. Paris , 329 : 973 – 978 .
   Web of Science ®Google Scholar
• Kombe , I . 2004 . The linear heat equation with highly oscillating potential . Proc. Amer. Math. Soc. , 132 : 2683 – 2691 .
   Google Scholar
• Goldstein , JA and Zhang , QIS . 2002 . Linear parabolic equations with strong singular potentials . Trans. Amer. Math. Soci. , 355 : 197 – 211 .
   Google Scholar
• Goldstein , JA and Kombe , I . 2003 . Nonlinear degenerate parabolic equations with singular lower-order term . Adv. Diff. Eqns. , 8 : 1153 – 1192 .
   Google Scholar
• Goldstein , JA and Kombe , I . 2005 . Nonlinear degenerate parabolic equations on the Heisenberg group . Int. J. Evol. Eqn. , 1 : 1 – 22 .
   Google Scholar
• Kombe , I . 2006 . On the nonexistence of positive solutions to nonlinear degenerate parabolic equations with singular coefficients . Appl. Anal. , 85 : 467 – 478 .
   Google Scholar
• Kombe , I . 2006 . Nonlinear degenerate parabolic equations for Baouendi-Grushin operators . Math. Nachr. , 279 : 756 – 773 .
   Google Scholar
• Aguilar Crespo , JA and Alonso , IP . 2000 . Global behavior of the Cauchy problem for some critical nonlinear parabolic equations . SIAM J. Math. Anal. , 31 : 1270 – 1294 .
   Google Scholar
• Aglio , AD , Giachetti , D and Peral , I . 2004 . Results on parabolic equations related to some Caffarelli Kohn-Nirenberg inequalities . SIAM J. Math. Anal. , 36 : 691 – 716 .
   Google Scholar
• Garcia Azoreno , JP and Peral Alonso , I . 1998 . Hardy inequalities and some critical elliptic and parabolic problem . J. Diff. Eqns. , 144 : 441 – 476 .
   Google Scholar
• Abdellaoui , B , Colorado , E and Peral , I . 2004 . Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalities . J. Eur. Soc. (JEMS) , 6 : 119 – 148 .
   Google Scholar
• Caffarelli , L , Kohn , R and Nirenberg , L . 1984 . First order interpolation inequalities with weights . Comp. Math. , 53 : 259 – 275 .
   Web of Science ®Google Scholar
• Capogna , L , Danielli , D and Garofalo , N . 1993 . An embedding theorem and the Harnack inequality for nonlinear subelliptic equations . Commun. Partial Diff. Eqns. , 18 : 1765 – 1794 .
   Web of Science ®Google Scholar
• Hörmander , L . 1967 . Hypoelliptic second order differential equations . Acta Math. , 119 : 147 – 171 .
   Web of Science ®Google Scholar
• Folland , GB . 1973 . A fundamental solution for a subelliptic operator . Bull. Amer. Math. Soc. , 79 : 373 – 376 .
   Web of Science ®Google Scholar
• Garofalo , N and Lanconelli , E . 1990 . Frequency functions on the Heisenberg group the uncertanly principle and unique continuation . Ann. Inst. Fourier Grenoble , 40 : 313 – 356 .
   Web of Science ®Google Scholar
• Garofalo , N and Lanconelli , E . 1992 . Existence and nonexistence results for semilinear equations on the Heisenberg group . Indian Univ. Math. J. , 41 : 71 – 98 .
   Web of Science ®Google Scholar
• Beals , R , Gaveau , B and Greiner , P . 1996 . On a geometric formula for the fundamental solution of subelliptic laplacians . Math. Nachr. , 181 : 81 – 163 .
   Web of Science ®Google Scholar
• Beals , R , Gaveau , B and Greiner , P . 1999 . Green's functions for some highly degenerate elliptic operators . J. Funct. Anal. , 165 : 407 – 429 .
   Web of Science ®Google Scholar
• Zhang , H and Niu , P . 2003 . Hardy-type inequalities and Pohozaev type identities for a class of p-degenerate subelliptic operators and applications . Nonlin. Anal. , 54 : 165 – 186 .
   Google Scholar
• Niu , P , Zhang , H and Wang , Y . 2001 . Hardy type and Rellich type inequalities on the Heisenberg group . Proc. Amer. Math. Soc. , 129 : 3623 – 3630 .
   Web of Science ®Google Scholar
• Goldstein , JA and Kombe , I . 2007 . The Hardy inequality and nonlinear parabolic equations on Carnot groups . Nonlin. Anal. , (doi:10.1016/j.na.2007.11.020, in press)
   Google Scholar
• Kombe , I . Hardy and Rellich type inequalities with remainders for Baouendi-Grushin vector fields (Preprint) .
   Google Scholar