Integrability for vector-valued minimizers of some variational integrals
Leonetti, Francesco ; Siepe, Francesco
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 469-479 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We prove that the higher integrability of the data $f, f_0$ improves on the integrability of minimizers $u$ of functionals $\Cal F$, whose model is $$ \int_{\Omega} \left[|Du|^p + (\operatorname{det} (Du))^2 - \langle f,Du \rangle + \langle f_0,u \rangle \right] dx, $$ where $u:\Omega\subset \Bbb R^n\to \Bbb R^n$ and $p\ge 2$.

Publié le : 2001-01-01
Classification:  35J20,  35J60,  49J20,  49J53,  49N60 
@article{119261,
     author = {Francesco Leonetti and Francesco Siepe},
     title = {Integrability for vector-valued minimizers of some variational integrals},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {469-479},
     zbl = {1051.49023},
     mrnumber = {1860235},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119261}
}

Leonetti, Francesco; Siepe, Francesco. Integrability for vector-valued minimizers of some variational integrals. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 469-479. http://gdmltest.u-ga.fr/item/119261/

Boccardo L.; Giachetti D. Alcune osservazioni sulla regolarità delle soluzioni di problemi fortemente non lineari e applicazioni, Ricerche Mat. XXXIV (1985), 309-323. (1985) | MR 0870828

Boccardo L.; Schianchi R. A remark on the $L^s$-regularity of the minima of functionals of the calculus of variations, Rev. Mat. Univ. Complut. Madrid 2 (1989), 113-118. (1989) | MR 1012107

Campanato S. Sistemi ellittici in forma di divergenza, Quaderni Scuola Norm. Sup. Pisa, 1980. | MR 0668196

De Giorgi E. Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. Un. Mat. Ital. 4 (1968), 135-137. (1968) | MR 0227827

D'Ottavio A.; Leonetti F.; Musciano C. Maximum principle for vector-valued mappings minimizing variational integrals, Atti Sem. Mat. Fis. Univ. Modena, suppl. vol. XLVI (1998), 677-683. (1998) | MR 1645746 | Zbl 0913.35026

Fusco N.; Hutchinson J. Partial regularity and everywhere continuity for a model problem from non-linear elasticity, J. Austral. Math. Soc. (Series A) 57 (1994), 158-169. (1994) | MR 1288671

Giachetti D.; Porzio M.M. Local regularity results for minima of functionals of the calculus of variations, Nonlinear Anal. TMA 39 (2000), 463-482. (2000) | MR 1725398

Giaquinta M. Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. of Math. Stud. 105, Princeton Univ. Press, 1983. | MR 0717034 | Zbl 0516.49003

Giusti E. Metodi diretti nel calcolo delle variazioni, U.M.I., 1994. | MR 1707291 | Zbl 0942.49002

Kufner A.; John O.; Fučik S. Function Spaces, Noordhoff International Publishing, Leyden, 1977. | MR 0482102

Leonetti F. Maximum principle for vector-valued minimizers of some integral functionals, Boll. Un. Mat. Ital. 7 (1991), 51-56. (1991) | MR 1101010 | Zbl 0729.49015

Leonetti F. Maximum principle for functionals depending on minors of the jacobian matrix of vector-valued mappings, Australian Nat. Univ., Centre for Math. Anal., Research Report 20, 1990.

Nečas J.; Stará J. Principio di massimo per i sistemi ellittici quasi lineari non diagonali, Boll. Un. Mat. Ital. 6 (1972), 1-10. (1972) | MR 0315281

Stampacchia G. Equations elliptiques du second ordre à coefficientes discontinus, Semin. de Math. Supérieures, Univ. de Montréal 16 (1966). (1966) | MR 0251373