Regularity, monotonicity and symmetry of positive solutions of m-Laplace equations

By Lucio Damascelli, Berardino Sciunzi. 2004

233 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9566a12662c4f4d5a6a26c11e54b34c613e2bf8e

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Radial symmetry and applications for a problem involving the $-\Delta_p(\cdot)$ operator and critical nonlinearity in~$\mathbb{R}^N$ (2014, methodology): “s not possible that u< uλ0 in every connected component C of Σλ0 \Zλ0. Suppose by contradiction that u<uλ0 in Σλ0 \ Zλ0 and let η>0 be arbitrarily small (to be ﬁxed later). By the results in [11], [36] and [37], we know that L(Zu) = 0,where L(A) is the Lebesgue measure of a set A. This and ”
Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of m-laplace equations (2006, methodology): “1) (see [11] and the references therein) we prove regularity results for solutions in general domains.”
Interior regularity results for inhomogeneous anisotropic quasilinear equations (2021, result): “We also refer to [10] for an earlier contribution under stronger regularity assumptions on both u and f .”
On viscosity and weak solutions for non-homogeneous p-Laplace equations (2016, background): “or more details. It is worth to mention that many equations appearing in the literature have the structure of (1.1) with lower order term satisfying the above assumptions on f. We refer the reader to [14, 15, 3, 2] and the references therein for examples of such f. The paperis organized as follows: ”
Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems (2017, background): “Moreover, they either just deal with local solutions [4,46], or entail smoothness assumptions on ∂ [26].”
Monotonicity and one-dimensional symmetry for solutions of −Δpu = f(u) in half-spaces (2011, methodology): “Let us recall that the linearized operator Lu(v, φ) at a fixed solution u of − p(u) = f (u) is well defined, for every v, φ ∈ H1,2 ρ ( ) with ρ ≡ |∇u|p−2(see [8] for details), by Lu(v, φ) ≡ ∫ [|∇u|p−2(∇v,∇φ)+ (p − 2)|∇u|p−4(∇u,∇v)(∇u,∇φ)− f ′(u)vφ]dx Moreover, v ∈ H1,2 ρ ( ) is a weak solution of th”
Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces (2012, methodology): “ase p > 2 is more complicated than the case 1 < p < 2 since the use of the classic Poincar´e inequality has to be replaced by the use of a weighted Poicar´e type inequality, in the spirit of [DS1]. However, the constants in the weighted Poicar´e type inequality developed in [DS1] depend upo”