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2 votes
1 answer
169 views

What rotations are used as a reduction step in Kenig-Ruiz-Sogge's uniform Sobolev estimate?

I think I have understood the bulk of the paper [KRS], but one of the parts I cannot understand is when the authors reduce Theorem 2.1 (p.332) into Proposition 2.1 (p.335). I can understand all the ...
Calvin Khor's user avatar
2 votes
0 answers
153 views

Uniqueness of the solution to systems of first-order linear PDEs

Context: Let $\Omega \subset \mathbb{R}^p$ be an domain. For functions $A_{jk}^i : \Omega \to \mathbb{R}$ and $B_k^i : \Omega \to \mathbb{R}$ with some regularity, I am interested in the following ...
Paruru's user avatar
  • 51
0 votes
0 answers
46 views

Uniqueness results for linear first order systems of PDEs

Context: I have the following system of PDEs, for an unknown function $u:\mathbb{R}^{n+1}\to \mathbb{C}^m$ (it is a system in the components of $u$): $$u_{x_0}=\sum_{i=1}^n A_iu_{x_i} + B(x)u\qquad u(...
Samuele's user avatar
  • 1,205