Everywhere regularity for a class of elliptic systems without growth conditions

 Access to full text

 Full (PDF)

1. [1] E. Acerbi - N. Fusco, Partial regularity under anisotropic (p,q) growth conditions, J. Differential Equations107 (1994), 46-67. Zbl0807.49010MR1260848
2. [2] T. Bhattacharya - F. Leonetti, W2,2 regularity for weak solutions of elliptic systems with nonstandard growth, J. Math. Anal. Appl.176 (1993), 224-234. Zbl0809.35008MR1222166
3. [3] M. Chipot - L.C. Evans, Linearization at infinity and Lipschitz estimates for certain problems in the calculus of variations, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), 291-303. Zbl0602.49029MR852362
4. [4] H.J. Choe, Interior behaviour of minimizers for certain functionals with nonstandard growth, Nonlinear Anal. Theory Methods Appl.19 (1992), 933-945. Zbl0786.35040MR1192273
5. [5] E. De Giorgi, Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. Un. Mat. Ital.1 (1968), 135-137. Zbl0155.17603MR227827
6. [6] E. Di Benedetto, C1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. Theory Methods Appl.7 (1983), 827-850. Zbl0539.35027
7. [7] D.M. Duc - J. Eells, Regularity of exponentially harmonic functions, Internat. J. Math.2 (1991), 395-408. Zbl0751.58007MR1113568
8. [8] L.C. Evans, A new proof of local C1,α regularity for solutions of certain degenerate elliptic p.d.e., J. Differential Equations45 (1982), 356-373. Zbl0508.35036
9. [9] N. Fusco - C. Sbordone, Higher integrability of the gradient of minimizers of functionals with nonstandard growth conditions, Comm. Pure Appl. Math.43 (1990), 673-683. Zbl0727.49021MR1057235
10. [10] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Math. Studies105, Princeton Univ. Press, Princeton NJ, 1983. Zbl0516.49003MR717034
11. [11] M. Giaquinta - G. Modica, Remarks on the regularity of the minimizers of certain degenerate functionals, Manuscripta Math.57 (1986), 55-99. Zbl0607.49003MR866406
12. [12] E. Giusti, Regolarità parziale delle soluzioni di sistemi ellittici quasi lineari di ordine arbitrario, Ann. Scuola Norm. Sup. Pisa Cl. Sci.23 (1969), 115-141. Zbl0175.40102MR247258
13. [13] E. Giusti - M. Miranda, Un esempio di soluzioni discontinue per un problema di minimo relativo ad un integrale regolare del calcolo delle variazioni, Boll. Un. Mat. Ital.2 (1968), 1-8. Zbl0155.44501MR232265
14. [14] E. Giusti - M. Miranda, Sulla regolarità delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari, Arch. Rational Mech. Anal.31 (1968), 173-184. Zbl0167.10703MR235264
15. [15] O. Ladyzhenskaya - N. Ural'tseva, Linear and quasilinear elliptic equations, in "Mathematics in Science and Engineering", Vol. 46, Academic Press, San Diego, 1968. Zbl0164.13002MR244627
16. [16] J. Lewis, Regularity of derivatives of solutions to certain degenerate elliptic equations, IndianaUniv. Math. J.32 (1983), 849-858. Zbl0554.35048MR721568
17. [17] G.M. Lieberman, On the regularity of the minimizer of a functional with exponential growth, Comment. Math. Univ. Carolin.33 (1992), 45-49. Zbl0776.49026MR1173745
18. [18] G.M. Lieberman, Gradient estimates for a class of elliptic systems, Ann. Mat. Pura Appl.164 (1993), 103-120. Zbl0819.35019MR1243951
19. [19] J.J. Manfredi, Regularity for minima of functionals with p-growth, J. Differential Equations76 (1988), 203-212. Zbl0674.35008MR969420
20. [20] P. Marcellini, Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions, Arch. Rational Mech. Anal.105 (1989), 267-284. Zbl0667.49032MR969900
21. [21] P. Marcellini, Regularity and existence of solutions of elliptic equations with p, q-growth conditions, J. Differential Equations90 (1991), 1-30. Zbl0724.35043MR1094446
22. [22] P. Marcellini, Regularity for elliptic equations with general growth conditions, J. Differential Equations105 (1993), 296-333. Zbl0812.35042MR1240398
23. [23] E. Mascolo - G. Papi, Local boundedness of minimizers of integrals of the calculus of variations, Ann. Mat. Pura Appl.167 (1994), 323-339. Zbl0819.49023MR1313560
24. [24] C.B. Morrey, Partial regularity results for non-linear elliptic systems, J. Math. and Mech.17 (1968), 649-670. Zbl0175.11901MR237947
25. [25] J. Ne, Example of an irregular solution to a nonlinear elliptic system with analytic coefficients and conditions for regularity, Theory of Nonlinear Operators, Abhandlungen der Akad. der Wissen. der DDR, 1977. Proc. of a Summer School held in Berlin in 1975. Zbl0372.35031MR509483
26. [26] J.P. Raymond, Lipschitz regularity of solutions of some asymptotically convex problems, Proc. Royal Soc. Edinburgh Sect. A 117 (1991), 59-73. Zbl0725.49012MR1096219
27. [27] G. Talenti, Boundedness of minimizers, Hokkaido Math. J.19 (1990), 259-279. Zbl0723.58015MR1059170
28. [28] P. Tolksdorff, Everywhere regularity for some quasilinear systems with a lack of ellipticity, Ann. Mat. Pura Appl.134 (1983), 241-266. Zbl0538.35034MR736742
29. [29] K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Math.138 (1977), 219-240. Zbl0372.35030MR474389

1. F. Leonetti, E. Mascolo, F. Siepe, Gradient regularity for minimizers of functionals under $p$-$q$ subquadratic growth
2. Elvira Mascolo, Anna Paola Migliorini, Everywhere regularity for vectorial functionals with general growth
3. Michael Bildhauer, Martin Fuchs, Xiao Zhong, A regularity theory for scalar local minimizers of splitting-type variational integrals
4. Emilio Acerbi, Giuseppe Mingione, Regularity results for a class of quasiconvex functionals with nonstandard growth
5. Elvira Mascolo, Anna Paola Migliorini, Everywhere regularity for vectorial functionals with general growth
6. Lars Diening, Bianca Stroffolini, Anna Verde, Lipschitz regularity for some asymptotically convex problems
7. Giuseppe Mingione, Zatorska-Goldstein Anna, Xiao Zhong, On the Regularity of p-Harmonic Functions in the Heisenberg Group
8. Menita Carozza, Antonia Passarelli di Napoli, Partial regularity for anisotropic functionals of higher order
9. Lars Diening, Bianca Stroffolini, Anna Verde, Lipschitz regularity for some asymptotically convex problems
10. Sabine Schemm, Partial regularity of minimizers of higher order integrals with (, )-growth