A Bernstein problem for special Lagrangian equations by Yuan Y. PDF

By Yuan Y.

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Sample text

D'- 0 I (c al - 2 + 2 + (wI - 0) ) + -2 c(w l points where s ~ 0, s ~ w(w~ - 0) , W2Jl < l pJ P p - 0) if and only if I+ P + (w+ 1 0)2 + W( w 1 - 0) + l w(w this directly but we omit the tedious is violated. 17) is violated £Q. 18) is valid. 22). 1 follows easily. d a 2 ~ 0, this can IIvII ~. 19) that + + a Lv IF+,n 120 + IF-,n I~ + (g}20 ,n is finite. 13) on the coefficients guarantees of unity systems which flatten the boundary. 11), by utilizing ~k' locally to a half-space a standard partition where supp ¢~ [-2, 2J.

2 then -m1 T));;;. 01, (a(x, Dx' ,,-;;;C(v)o 0 >0 T))v, v)o;;;. ) J boundary depends _d_ + dd t dXj conditions continuously on La satisfies that Ial stants the block structure ± IK 01' homogeneous I < EO °> ° 2 where assumption EO is sufficiently and a matrix-valued -1 + aN) is Hermitian * - 01 KKKK + R(~ + ~) small. function of degree zero with repsect to R(~ form Appendix B. Also, suppose Then there are con- K), R(xN, x', t, ~, w, n, a, (~, w, n) such that the following • ~ 011 , N-l (3) L Re(R((i~+n)I+ iWj(f:'j+aj)))~02rn, Ixl+ltl";;;TO+RO j=l (4) Fix s with are finite.

27) J (;~)w) ~I + (n + B)w)) d~ (w, Rw) A I ;;;. 2, Proposition N-l + ~ )-l( \' dW dW (n + B)w) j~l Aj dX + + j at 'I A-l, where p(XN' x' Ixl + It perties I t) ~RO. 17) to obtain that provided > C2. 7) provided --) vj,k' vj,k .

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A Bernstein problem for special Lagrangian equations by Yuan Y.


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