A Note on Riviere, S Conjecture

Xianjiang Jiang ； Ruyi Quan

《International Journal of Social Science and Education Research》 4卷12期 (2021/12) Pp. 541-545

https://doi.org/10.6918/IJOSSER.202112_4(12).0080

摘要

In this note,we consider the equations Δu= Ω∇u with the unknown vector ^(u∈W^(1,2)) (B_1^n, R^m). here Ω = (Ω_j^i)_(1≤I, j≤m)∈ L^2(R^n, R^m) If there exists a matrix valued function A,A^(-1)∈W^(1,2)(R^n)?L^∞(R^n), such that Ω = -A∇A^-, then the solution u∈W^(2,1)(B_(1/4)^n). In particular, the equations Δu =Ω∇u with u, θ∈W^(2,1)(B_1^n, R^m), Ω= (The equation is abbreviated), then the solution u ∈W^(2,1)(B_(1/4)^n).

關鍵字

Conservation laws ； Non‐linear elliptic systems ； Harmonic maps 2010 MR Subject Classification 00A99 ； 97U60 ； 97U70

參考文獻

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