Partial regularity for minima of variational integrals
نویسندگان
چکیده
منابع مشابه
A simple partial regularity proof for minimizers of variational integrals
We consider multi-dimensional variational integrals F [u] := Ω f (·, u, Du) dx where the integrand f is a strictly convex function of its last argument. We give an elementary proof for the partial C 1,α-regularity of minimizers of F. Our approach is based on the method of A-harmonic approximation, avoids the use of Gehring's lemma, and establishes partial regularity with the optimal Hölder expo...
متن کاملBoundary regularity results for variational integrals
We prove partial Hölder continuity for the gradient of minimizers u ∈W (Ω,R ), Ω ⊂ R a bounded domain, of variational integrals of the form
متن کاملPartial Regularity for Almost Minimizers of Quasi-Convex Integrals
We consider almost minimizers of variational integrals whose integrands are quasiconvex. Under suitable growth conditions on the integrand and on the function determining the almost minimality, we establish almost everywhere regularity for almost minimizers and obtain results on the regularity of the gradient away from the singular set. We give examples of problems from the calculus of variatio...
متن کاملExistence and Lipschitz Regularity for Minima
We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional
متن کاملPARTIAL REGULARITY FOR MINIMA OF HIGHER ORDER FUNCTIONALS WITH p(x) GROWTH
Ω f (x, δw(x), Dw(x)) dx, on the space W loc (Ω;R N ), N > 1, where Ω ⊂ R is an open bounded domain and f : Ω × R × R nN×. . .×RN(n+m−1 m ) → R a Carathéodory function. δw ≡ (w,Dw, . . . , Dw) denotes the vector containing the lower order derivatives. For k = 1, . . . ,m we use the notation Du ≡ {Dui} i=1,...,N for the derivative of order k. Note that Du is an element of the space ⊙k(Rn;RN ) of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1987
ISSN: 0004-2080
DOI: 10.1007/bf02384445