| Title:
|
Boundedness and pointwise differentiability of weak solutions to quasi-linear elliptic differential equations and variational inequalities (English) |
| Author:
|
Ježková, Jana |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
63-80 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The local boundedness of weak solutions to variational inequalities (obstacle problem) with the linear growth condition is obtained. Consequently, an analogue of a theorem by Reshetnyak about a.e\. differentiability of weak solutions to elliptic divergence type differential equations is proved for variational inequalities. (English) |
| Keyword:
|
quasi-linear elliptic equations and inequalities |
| Keyword:
|
weak solution |
| Keyword:
|
local boundedness |
| Keyword:
|
pointwise differentiability |
| Keyword:
|
difference quotient |
| MSC:
|
35B65 |
| MSC:
|
35D10 |
| MSC:
|
35J60 |
| MSC:
|
35J85 |
| MSC:
|
35R45 |
| idZBL:
|
Zbl 0803.35061 |
| idMR:
|
MR1292584 |
| . |
| Date available:
|
2009-01-08T18:08:51Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118642 |
| . |
| Reference:
|
[1] Bojarski B.: Pointwise differentiability of weak solutions of elliptic divergence type equations.Bull. Acad. Polon. Sci. 33 (1985), 1-6. Zbl 0572.35011, MR 0798721 |
| Reference:
|
[2] Federer H.: Geometric Measure Theory.Springer-Verlag, Berlin-Heidelberg-New York, 1969. Zbl 0874.49001, MR 0257325 |
| Reference:
|
[3] Giaquinta M.: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems.Princeton University Press, Princeton, New Jersey, 1983. Zbl 0516.49003, MR 0717034 |
| Reference:
|
[4] Hajłasz P., Strzelecki P.: A new proof of Reshetnyak's theorem concerning the pointwise differentiability of solution of quasilinear equations.Preprint, Institute of Mathematics, Warsaw University, PKIN IXp., 00-901 Warsaw. |
| Reference:
|
[5] Ladyzhenskaya O.A., Ural'tseva N.N.: Linear and Quasilinear Elliptic Equations.2nd ed., Nauka Press, Moscow, 1973, English translation Academic Press, New York, 1968. Zbl 0177.37404, MR 0244627 |
| Reference:
|
[6] Moser J.: A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations.Comm. Pure Appl. Math. XIII (1960), 457-468. Zbl 0111.09301, MR 0170091 |
| Reference:
|
[7] Moser J.: On Harnack's theorem for elliptic differential equations.Comm. Pure Appl. Math. XIV (1961), 577-591. Zbl 0111.09302, MR 0159138 |
| Reference:
|
[8] Reshetnyak Yu.G.: Generalized derivatives and differentiability almost everywhere.Mat. Sb. 75 (117) (1968), 323-334 (in Russian) Math. USSR-Sb. 4 (1968), 293-302 (English translation). Zbl 0176.12001, MR 0225159 |
| Reference:
|
[9] Reshetnyak Yu.G.: O differentsiruemosti pochti vsyudu resheniĭ ellipticheskikh uravneniĭ.Sibirsk. Mat. Zh. XXVIII (1987), 193-195. MR 0906049 |
| Reference:
|
[10] Serrin J.: Local behavior of solutions of quasi-linear equations.Acta Math. 111 (1964), 247-302. Zbl 0128.09101, MR 0170096 |
| Reference:
|
[11] Stepanoff M.W.: Sur les conditions de l'existence de la différentielle totale.Matematiceskij Sbornik, Rec. Math. Soc. Math. Moscou XXXII (1925), 511-527. |
| Reference:
|
[12] Ziemer W.P.: Weakly Differentiable Functions.Springer-Verlag, Berlin-Heidelberg-New York, 1989. Zbl 0692.46022, MR 1014685 |
| . |
