DIFFUSION COEFFICIENTS ESTIMATION FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS Academic Article uri icon

abstract

  • 2017 Society for Industrial and Applied Mathematics. This paper considers the Dirichlet problem -div(aua) = f on D, ua = 0 on D, for a Lipschitz domain D d, where a is a scalar diffusion function. For a fixed f, we discuss under which conditions a is uniquely determined and when a can be stably recovered from the knowledge of ua. A first result is that whenever a H1(D), with 0 < a on D, and f L(D) is strictly positive, then a - bL2(D) Cua - ubH01(D)1/6. More generally, it is shown that the assumption a H1(D) can be weakened to a Hs(D), for certain s < 1, at the expense of lowering the exponent 1/6 to a value that depends on s.

published proceedings

  • SIAM JOURNAL ON MATHEMATICAL ANALYSIS

author list (cited authors)

  • Bonito, A., Cohen, A., DeVore, R., Petrova, G., & Welper, G.

complete list of authors

  • Bonito, Andrea||Cohen, Albert||DeVore, Ronald||Petrova, Guergana||Welper, Gerrit

publication date

  • January 1, 2017 11:11 AM