Complutense University Library

Local vanishing properties of solutions of elliptic and parabolic quasilinear equations


Díaz Díaz, Jesús Ildefonso and Véron, Laurent (1985) Local vanishing properties of solutions of elliptic and parabolic quasilinear equations. Transactions of the American Mathematical Society, 290 (2). pp. 787-814. ISSN 0002-9947

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:


This paper is a study of some vanishing properties of weak solutions to nonlinear elliptic and parabolic equations. Instead of using monotonicity arguments, the method of proof is based on an energy method.

Item Type:Article
Uncontrolled Keywords:weak solutions; quasilinear equations; local vanishing
Subjects:Sciences > Mathematics > Differential equations
ID Code:16417

R. A.Adams, Sobolev spaces,Academic Press, New York, 1975.

H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311-341

S. N. Antoncev, On the localization of solutions of nonlinear degenerate elliptic and parabolic equations, Soviet Math. Dokl. 24 (1981), 420-424.

R. Aris, The mathematical theory of diffusion and reaction in permeable catalysts, Clarendon Press, Oxford, 1975.

C. Atkinson and J. E. Bouillet, Some qualitative properties of solutions of a generalized diffusion equation, Math. Proc. Cambridge Philos. Soc. 86 (1979), 495-510. H.

Attouch and A. Damlamian, Application des méthodes de convexité et monotonie à l'étude de certaines équations quasilinéaires, Proc. Roy. Soc. Edinburgh Sect. A 79 (1977), 107-129.

A. Bamberger, Etude d'une équation doublement non linéaire, J. Funct. Anal. 24 (1977), 148-155.

Ph. Benilan, H. Brezis and M. G. Crandall, A semilinear equation in L1 (RN), Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (1975), 523-555.

M. F. Bidaut-Veron, Variational inequalities of order 2m in unbounded domains, Nonlinear Anal. 6 (1982), 253-269.

H. Brezis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to Nonlinear Functional Analysis (E. Zarantonello, ed.), Academic Press, New York, 1971.

H. Brezis, Solutions of variational inequalities with compact support, Uspekhi Mat. Nauk 129 (1974), 103-108.

H. Brezis and F. Browder, Strongly nonlinear elliptic boundary value problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)5 (1976), 587-603.

H. Brezis and A. Friedman, Estimates on the support of solutions of parabolic variational inequalities, Illinois J. Math. 20 (1976), 82-97.

J. I. Diaz, Solutions with compact support for some degenerate parabolic problems, Nonlinear Anal. 3 (1979), 831-847.

J. I. Diaz and J. Hernandez, Some results on the existence of free boundaries for parabolic reaction-diffusion systems, Trends in Theory and Practice of Nonlinear Differential Equations (V. Lakshmikantham, ed.), Dekker, New York, 1984.

J. I. Diaz and M. A. Herrero, Estimates on the support of the solutions of some nonlinear elliptic and parabolic problems, Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), 249-258.

J. I. Diaz and L. Veron, Existence theory and qualitative properties of the solutions of some first order quasilinear variational inequalities, Indiana Univ. Math. J. 32 (1983), 319-361.

M. E. Gurtin and R. C. Mac Camy, On the diffusion of biological populations, Math. Biosci. 33 (1977), 35-49.

A. S. Kalashnikov, On equations of the nonstationary-filtration type in which the perturbation is propagated at infinite velocity, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 6 (1972), 45-49.

A. S. Kalashnikov, The propagation of disturbances in problems of nonlinear heat conduction with absorption, Zh. Vychisl. Mat. i Mat. Fiz. 14 (1974), 891-905.

A. S. Kalashnikov, On a nonlinear equation appearing in the theory of non-stationary filtration, Trudy Sem. Petrovsk. 4 (1978), 137-146.

R. Kersner, The behaviour of temperature fronts in media with nonlinear thermal conductivity under absorption, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 33 (1978), 44-51.

R. Kersner, Filtration with absorption: necessary and sufficient conditions for the propagation of perturbations to have finite velocity (to appear).

R. Kersner, Nonlinear heat conduction with absorption: space localization and extinction in finite time (to appear).

B. F. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234 (1977), 381-415.

O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and quasilinear elliptic equations, Academic Press, New York, 1968.

O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Transl., vol. 23, 1968.

J. L. Lions, Quelques méthodes de résolutions des problèmes aux limites non linéaires, Dunod, Paris, 1969.

L. K. Martinson and K. B. Pavlov, The effect of magnetic plasticity in non-Newtonian fluids, Magnit. Gidrodinamika 3 (1969), 69-75.

L. K. Martinson and K. B. Pavlov, Unsteady shear flows of a conducting fluid with a rheological power law, Magnit. Gidrodinamika 4 (1970), 50-58.

O. A. Oleinik, A. S. Kalashnikov and C. Yui Lin, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration, Izv. Akad. Nauk SSSR Ser. Mat. 22 (1958), 667-704.

L. A. Peletier, A necessary and sufficient condition for the existence of an interface in flows through porous media, Arch. Rational Mech. Anal. 56 (1974), 183-190.

G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinus, Presses de l'Univ. de Montréal, 1966.

L. Veron, Equations d'évolution semi-linéaires du second ordre dans L1, Rev. Roumaine Math. Pures Appl. 27 (1982), 95-123.

L. Veron, Effets régularisants de semi-groupes non linéaires dans des espaces de Banach, Ann. Fac. Sci. Toulouse Math. (5) 1 (1979), 171-200.

Deposited On:18 Sep 2012 08:37
Last Modified:07 Feb 2014 09:29

Repository Staff Only: item control page