Abstract
In this paper we prove the local boundedness of minimizers of integral functionals with non-standard growth conditions.
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References
R. A. Adams,Sobolev Spaces, Academic Press, New York (1975).
N. Fusco -C. Sbordone,Higher integrability of the gradient of minimizers offunctionals with non standard growth conditions, Comm. Pure Appl. Math., XLIII, (1990), pp. 673–683.
M. Giaquinta,Multiple integrals in the calculus of variations and nonlinear elliptic system, Ann. Math. Studies,105, Princeton Univ. Press, Princeton (1983).
E. Giusti,Equazioni ellittiche del secondo ordine, Quaderni U.M.I.,6, Pitagora, Bologna (1978).
M. A.Krasnosel'skii - Y. A.Rutickii,Convex functions and Orlicz spaces, Noordhoff LTD (1961).
O. A.Ladyženskaja - N. N.Ural'ceva,Linear and quasilinear elliptic equations, Math. Sc. Eng.,46, Academic Press (1968).
P. Marcellini,Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions, Archive Rat. Mech. Anal,105 (5), (1989), pp. 267–284.
P. Marcellini,Regularity and existence of solutions of elliptic equations with p, q-growth conditions, J. Diff. Eqs.,90 (1991), pp. 1–30.
P. Marcellini,Regularity for elliptic equations with general growth conditions, J. Diff. Eq.,105 (1993), pp. 296–333.
Min-Chun Hong,Some remarks on the minimizers of variational integrals with non-standard growth conditions, Boll. U.M.I., (7),6-A (1992), pp. 91–101.
J. Moser,A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math.,13 (1960), pp. 457–468.
G. Moscariello -L. Nania,Hölder continuity of minimizers of functionals with non standard growth conditions, Ric. Mat., Vol.XL, II (1991), pp. 259–273.
M. M. Rao -Z. D. Ren,Theory of Orlicz Spaces, Pure and Appl. Math., Marcel Dekker, New York (1991).
G. Talenti,Boundedness of minimizers, Hokkaido Math. J.,19 (1990), pp. 259–279.
V. V. Zhikov,Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR-Izv.,29 (1987), pp. 33–66.
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Mascolo, E., Papi, G. Local boundedness of minimizers of integrals of the calculus of variations. Annali di Matematica pura ed applicata 167, 323–339 (1994). https://doi.org/10.1007/BF01760338
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DOI: https://doi.org/10.1007/BF01760338