A new partial regularity result for non-autonomous convex integrals with non-standard growth conditions

作者：De Maria Bruno; di Napoli Antonia Passarelli^*

来源：Journal of Differential Equations, 2011, 250(3): 1363-1385.

DOI：10.1016/j.jde.2010.09.033

• Variational integrals
• Non-standard growth conditions
• Partial regularity

We establish C(1,gamma)-partial regularity of minimizers of non-autonomous convex integral functionals of the type: F(u; Omega) := integral(Omega) f(x, Du)dx, with non-standard growth conditions into the gradient variable
1/L vertical bar xi vertical bar(p) <= f(x, xi) <= L(1+vertical bar xi vertical bar(q))
for a couple of exponents p, q such that
1 < p <= q < min{p n/n-1, p+1},
and alpha-Holder continuous dependence with respect to the x variable. The significant point here is that the distance between the exponents p and q is independent of a. Moreover this bound on the gap between the growth and the coercitivity exponents improves previous results in this setting.

• 出版日期2011-2-1