Boundedness of the extremal solution of some p-Laplacian problems

By Manel Sanchón. 2007

54 citations recorded by the source corpus.

In this article we consider the p-Laplace equation −Δpu=λf(u) on a smooth bounded domain of RN with zero Dirichlet boundary conditions. Under adequate assumptions on f we prove that the extremal solution of this problem is in the energy class W01,p(Ω) independently of the domain. We also obtain Lq and W1,q estimates for such a solution. Moreover, we prove its boundedness for some range of dimensions depending on the nonlinearity f.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ba9a5a3260d550b140fbeb36e4482303b2c27016

Citations in the corpus

• The extremal solution for the fractional Laplacian (2013, unknown): “Then, for every ∈ (0, 1− τ) there exists a positive constant C such that f(t) ≤ C(1 + t) 1 1−(τ+ ) , for all t > 0.”