PARTIAL REGULARITY FOR MINIMA OF HIGHER ORDER FUNCTIONALS WITH p(x) GROWTH
نویسنده
چکیده
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 symmetric k– linear forms on R with values in R which can be identified with the space R( n+k−1 k ). In the whole paper, for the seek of brevity we use the abbreviations M ≡ N ∑m−1 k=0 ( n+k−1 k ) and N ≡ N ( n+m−1 m )
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