Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations Articles uri icon

authors

  • LEONORI, TOMMASO
  • PERAL, IRENEO
  • PRIMO, ANA
  • SORIA, FERNANDO

publication date

  • December 2015

start page

  • 6031

end page

  • 6068

issue

  • 12- Número especial

volume

  • 35

International Standard Serial Number (ISSN)

  • 1078-0947

Electronic International Standard Serial Number (EISSN)

  • 1553-5231

abstract

  • In this work we consider the problems { Lu = f in Omega u = 0 in R-N\Omega, and {u(t) + Lu = f in Q(T) Omega x (0, T), u(x, t) = 0 in (R-N\Omega) x (0, T), u(x, 0) = 0 in Omega, where L is a nonlocal differential operator and Omega is a bounded domain in R-N, with Lipschitz boundary. The main goal of this work is to study existence, uniqueness and summability of the solution u with respect to the summability of the datum f. In the process we establish an L-p-theory, for p >= 1, associated to these problems and we prove some useful inequalities for the applications.

keywords

  • nonlocal operators; elliptic equations; parabolic equations; summability of the solutions