A Nonlocal p-Laplacian Evolution Equation with Nonhomogeneous Dirichlet Boundary Conditions

@article{Andreu2008ANP,
  title={A Nonlocal p-Laplacian Evolution Equation with Nonhomogeneous Dirichlet Boundary Conditions},
  author={F. Andreu and Jos{\'e} M. Maz{\'o}n and Julio D. Rossi and Juli{\'a}n Toledo},
  journal={SIAM J. Math. Analysis},
  year={2008},
  volume={40},
  pages={1815-1851}
}
Abstract. In this paper we study the nonlocal p-Laplacian-type diffusion equation ut(t, x) = ∫ RN J(x−y)|u(t, y)−u(t, x)|p−2(u(t, y)−u(t, x)) dy, (t, x) ∈]0, T [×Ω, with u(t, x) = ψ(x) for (t, x) ∈ ]0, T [×(RN \Ω). If p > 1, this is the nonlocal analogous problem to the well-known local p-Laplacian evolution equation ut = div(|∇u|p−2∇u) with Dirichlet boundary condition u(t, x) = ψ(x) on (t, x) ∈ ]0, T [×∂Ω. If p = 1, this is the nonlocal analogous to the total variation flow. When p = +∞ (this… CONTINUE READING
Highly Cited
This paper has 33 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 21 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 32 references

Variational models of sandpile growth

  • L. Prigozhin
  • Eur. J. Appl. Math., 7
  • 1996
Highly Influential
8 Excerpts

Completely accretive operators, In Semigroup Theory and Evolution Equations (Delft

  • Ph. Bénilan, M. G. Crandall
  • Lecture Notes in Pure and Appl. Math. 135,
  • 1989
Highly Influential
7 Excerpts

A nonlocal p-Laplacian evolution equation with Newmann boundary conditions

  • F. Andreu, J. M. Mazón, J. D. Rossi, J. Toledo
  • J. Math. Pures Appl., 90
  • 2008
8 Excerpts

Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

  • L. Caffarelli, S. Salsa, L. Silvestre
  • Inventiones Mathematicae, 171
  • 2008
1 Excerpt

Similar Papers

Loading similar papers…