We consider an optimization problem with volume constraint for an energy functional associated to an inhomogeneous operator with nonstandard growth. By studying an auxiliary penalized problem, we prove existence and ...

In this paper we obtain the Lipschitz continuity of nonnegative local minimizers of the functional J(v) = ∫ Ω - F(x; v; ∇v) + (x)νfv>0) dx, under nonstandard growth conditions of the energy function F(x; s; η) and 0 < λmin ...

In 1993, V. Šverák proved that if a sequence of uniformly bounded domains Ωn ℝ2 such that Ωn → Ω in the sense of the Hausdorff complementary topology, verify that the number of connected components of its complements are ...

In this article we study eigenvalues and minimizers of a fractional non-standard growth problem. We prove several properties on these quantities and their corresponding eigenfunctions.

We obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-Laplacian. Namely, ∆p(x)u := div |∇u| p(x)−2∇u = ...

We consider the existence of periodic solutions to Hamiltonian systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in ...

Coiled tubings are widely used in oil and gas industries. Fracture toughness test of coiled tubing is a challenge. Non-standard specimen has to be used due to its geometrical difficulties, ie small thickness and diameter. ...

We define the notion of nonlocal magnetic Sobolev spaces with nonstandard growth for Lipschitz magnetic fields. In this context we prove a Bourgain-Brezis- Mironescu type formula for functions in this space as well as for ...