Geodesic
On the Uniqueness Problem for Nonlinear Elliptic and Parabolic Equations
Informatics and Automation, Differential equations and dynamical systems, Tome 236 (2002), pp. 318-327.

Voir la notice de l'article provenant de la source Math-Net.Ru

The Dirichlet and the Cauchy–Dirichlet problems for second-order nonlinear elliptic and parabolic equations are studied in the case of strongly growing or degenerate leading coefficients. The solvability of the problems and the uniqueness of their solutions are proved, energy estimates and estimates for the maximum of the solutions are established. 
@article{TRSPY_2002_236_a31,
     author = {I. V. Skrypnik and G. Gaevsi},
     title = {On the {Uniqueness} {Problem} for {Nonlinear} {Elliptic} and {Parabolic} {Equations}},
     journal = {Informatics and Automation},
     pages = {318--327},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a31/}
}
TY  - JOUR
AU  - I. V. Skrypnik
AU  - G. Gaevsi
TI  - On the Uniqueness Problem for Nonlinear Elliptic and Parabolic Equations
JO  - Informatics and Automation
PY  - 2002
SP  - 318
EP  - 327
VL  - 236
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a31/
LA  - ru
ID  - TRSPY_2002_236_a31
ER  - 
%0 Journal Article
%A I. V. Skrypnik
%A G. Gaevsi
%T On the Uniqueness Problem for Nonlinear Elliptic and Parabolic Equations
%J Informatics and Automation
%D 2002
%P 318-327
%V 236
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a31/
%G ru
%F TRSPY_2002_236_a31
I. V. Skrypnik; G. Gaevsi. On the Uniqueness Problem for Nonlinear Elliptic and Parabolic Equations. Informatics and Automation, Differential equations and dynamical systems, Tome 236 (2002), pp. 318-327. http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a31/

[4] Alt H. W., Luckhaus S., “Quasilinear elliptic-parabolic differential equations”, Math. Ztsch., 183 (1981), 311–341 | MR

[5] Benilan Ph., Wittbold P., “On mild and weak solutions of elliptic-parabolic problems”, Adv. Diff. Equat., 1 (1996), 1053–1076 | MR

[6] Gajewski H., Gröger K., Zacharias K., Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akad. Verl., Berlin, 1974 | MR

[7] Gajewski H., “On a variant of monotonicity and its application to differential equations”, Nonlin. Anal. TMA, 22 (1994), 73–80 | DOI | MR | Zbl

[8] Gajewski H., Gröger K., “Reaction-diffusion processes of electrically charged species”, Math. Nachr., 177 (1996), 109–130 | DOI | MR | Zbl

[9] Gajewski H., Zacharias K., “Global behavior of reaction diffusion system modelling chemotaxis”, Math. Nachr., 195 (1998), 77–114 | MR | Zbl

[10] Gajewski H., Skrypnik I. V., To the uniquness problem for nonlinear elliptic equations, Preprint No 527, WIAS, Berlin, 1999 | MR

[11] Moser J., “A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations”, Commun. Pure and Appl. Math., 13 (1960), 457–468 | DOI | MR | Zbl

[12] Otto F., “$L^1$-contraction and uniqueness for quasilinear elliptic-parabolic equations”, C. R. Acad. Sci. Paris. Sér. 1, 318 (1995), 1005–1010 | MR

[13] Skrypnik I. V., Methods of analysis of nonlinear elliptic boundary value problems, Transl. Math. Monogr., 139, Amer. Math. Soc., Providence, RI, 1994 | MR | Zbl