Differentiability and higher integrability results for local minimizers of splitting-type variational integrals in 2D with applications to nonlinear Hencky-materials
نویسندگان
چکیده
We prove higher integrability and differentiability results for local minimizers u: R2 ⊃ Ω → RM , M ≥ 1, of the splitting-type energy Ω[h1(|∂1u|) + h2(|∂2u|)] dx. Here h1, h2 are rather general N -functions and no relation between h1 and h2 is required. The methods also apply to local minimizers u: R2 ⊃ Ω → R2 of the functional ∫ Ω[h1(|div u|) + h2(|ε(u)|)] dx so that we can include some variants of so-called nonlinear Hencky-materials. Further extensions concern non-autonomous problems.
منابع مشابه
Twodimensional Variational Problems With A Wide Range Of Anisotropy
We consider local minimizers u : R 2 ⊃ Ω → R M of the variational integral Ω H(∇u) dx with density H growing at least quadratically and allowing a very large scale of anisotropy. We discuss higher integrability properties of ∇u as well as the differentiability of u in the classical sense. Moreover, a Liouville-type theorem is established.
متن کاملVariational integrals with a wide range of anisotropy
We consider anisotropic variational integrals of (p, q)-growth and prove for the scalar case interior C-regularity of bounded local minimizers under the assumption that q ≤ 2p by the way discussing a famous counterexample of Giaquinta. In the vector case we obtain some higher integrability result for the gradient.
متن کاملA remark on the regularity of vector-valued mappings depending on two variables which minimize splitting-type variational integrals
We combine a maximum principle for vector-valued mappings established by D’Ottavio, Leonetti and Musciano [DLM] with regularity results from [BF3] and prove the Hölder continuity of the first derivatives for local minimizers u: Ω → RN of splitting-type variational integrals provided Ω is a domain in R2. Roughly speaking, anisotropic variational integrals ∫ Ω F (∇u) dx with integrand F (∇u) of (...
متن کاملHigher integrability of the gradient for vectorial minimizers of decomposable variational integrals
We consider local minimizers u: Rn ⊃ Ω → RN of variational integrals I[u] := ∫ Ω F (∇u) dx, where F is of anisotropic (p, q)-growth with exponents 1 < p ≤ q < ∞. If F is in a certain sense decomposable, we show that the dimensionless restriction q ≤ 2p+2 together with the local boundedness of u implies local integrability of ∇u for all exponents t ≤ p+2. More precisely, the initial exponents fo...
متن کاملPartial Regularity for Degenerate Variational Problems and Image Restoration Models in Bv
We establish partial and local C1,α-regularity results for vectorial almost-minimizers of convex variational integrals in BV. In particular, we investigate cases with a degenerate or singular behavior of p-Laplace type, and we cover (local) minimizers of the exemplary integrals ∫
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008