Boundedness and higher integrability of minimizers to a class of two-phase free boundary problems under non-standard growth conditions.

In this paper, we are concerned with the existence, boundedness, and integrability of minimizers of heterogeneous, two-phase free boundary problems J_γ(u) = ∫_Ω (f(x, ∇u) + λ₊(u⁺)^γ + λ₋(u⁻)^γ + gu) dx → min under non-standard growth conditions. Included in such problems are heterogeneous jets and cavities of Prandtl-Batchelor type with γ = 0, chemical reaction problems with 0 < γ < 1, and obstacle type problems with γ = 1, respectively. [ABSTRACT FROM AUTHOR]