Regularity Results for a Class of Functionals with Non-Standard Growth

Abstract: We consider the integral functional under non-standard growth assumptions that we call p(x) type: namely, we assume that a relevant model case being the functional Under sharp assumptions on the continuous function p(x)>1 we prove regularity of minimizers. Energies exhibiting this growth appear in several models from mathematical physics.

[1]  Kumbakonam R. Rajagopal,et al.  On the modeling of electrorheological materials , 1996 .

[2]  Paolo Marcellini.  Regularity and existence of solutions of elliptic equations with p,q-growth conditions , 1991 .

[3]  G. Mingione,et al.  Regularity results for minimizers of irregular integrals with (p,q) growth , 2002 .

[4]  Dun Zhao,et al.  A class of De Giorgi type and Hölder continuity , 1999 .

[5]  N. Fusco,et al.  A transmission problem in the calculus of variations , 1994 .

[6]  Giuseppe Mingione,et al.  Hölder continuity of the gradient of p(x)-harmonic mappings , 1999 .

[7]  I. Fonseca,et al.  An existence result for a nonconvex variational problem via regularity , 2002 .

[8]  M. Rao,et al.  Theory of Orlicz spaces , 1991 .

[9]  M. Růžička.  Flow of shear dependent electrorheological fluids , 1999 .

[10]  Lawrence C. Evans,et al.  Quasiconvexity and partial regularity in the calculus of variations , 1986 .

[11]  J. Manfredi.  Regularity for minima of functionals with p-growth , 1988 .

[12]  N. Fusco,et al.  A regularity theorem for minimizers of quasiconvex integrals , 1987 .

[13]  V. Zhikov,et al.  Homogenization of Differential Operators and Integral Functionals , 1994 .

[14]  Zhikov.  On Lavrentiev's Phenomenon. , 1995 .

[15]  T. Iwaniec,et al.  On the Operator L(f)=f log |f| , 1999 .

[16]  N. Fusco,et al.  Regularity for Minimizers of Non-quadratic Functionals: The Case 1 , 1989 .

[17]  Paolo Marcellini.  Regularity for some scalar variational problems under general growth conditions , 1996 .

[18]  E. Acerbi,et al.  Regularity results for a class of quasiconvex functionals with nonstandard growth , 2001 .

[19]  Enrico Giusti,et al.  On the regularity of the minima of variational integrals , 1982 .

[20]  Irene Fonseca,et al.  Regularity results for anisotropic image segmentation models , 1997 .

[21]  N. Fusco,et al.  Hölder Continuity of Local Minimizers , 1999 .

[22]  Paolo Marcellini,et al.  Everywhere regularity for a class of elliptic systems without growth conditions , 1996 .

[23]  Paolo Marcellini.  Regularity for Elliptic Equations with General Growth Conditions , 1993 .

[24]  Paolo Marcellini.  Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions , 1989 .

[25]  A. Coscia,et al.  Hölder continuity of minimizers of functionals with variable growth exponent , 1997 .