A nonlocal p-Laplacian evolution equation with Neumann boundary conditions

By Fuensanta Andreu, José M. Mazón, Julio D. Rossi, Julián Toledo. 2008

132 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a4229264f988f9bb08ab2e8aacf288639556e685

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On the principal eigenvalue of some nonlocal diffusion problems (2009, background): “This resemblance has been already observed for related problems in previous works, for instance in [ 2 ], [15] and [17].”
On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, background): “If the behaviour of λp(LΩ + a) with respect to a or Ω can be exhibited directly from the definition, the impact of scalings of the kernel is usually unknown and has been largely ignored in the literature except in some specific situations involving particular nonlocal dispersal operators defined in ”
Decay estimates for nonlocal problems via energy methods (2009, background): “This problem, with a convolution kernel, J(x, y) = G(x − y) was considered in [3] and [2] where the authors found existence, uniqueness and the convergence of the solutions to solutions of the local p−Laplacian evolution problem, vt = div(|∇v|p−2∇v) when a rescaling parameter (that measures the size”
Fractional p-Laplacian evolution equations (2016, background): “Here, to overcome this difficulty, we follow the same idea that we used in [3] and [4] (see also [5]) to study a similar problem but with a non-singular kernel, that is, we replace u(y)−u(x) |u(y)−u(x)| by an antisymmetric L ∞–function η(x, y) such that ‖η(·, ·)‖L∞(RN×RN ) ≤ 1 and η(x, y) ∈ sign(u(y”
A class of integral equations and approximation of p-Laplace equations (2010, methodology): “withtheDirichletboundarycondition u = g0 on ∂� ×(0, T )andtheinitialdata u(·,0) = u0. In [ 2 ], they have treated the evolution equation similar to (1.4), but with MD replaced by the operator MN defined by”