Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small

By V. Ferone, François Murat. 2000

140 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/452ed377e4090c5036c48f3d0c08b52aa3c3f587

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Nonlinear elliptic equations having a gradient term with natural growth (2006, background): “The classical references are [18] and [22]; since then, many authors have proved results for second order elliptic problems with lower order terms depending on the gradient: these works include, for instance, [4], [5], [6], [8], [13], [14], [15], [16], [20], [25], [27], or [29].”
Morrey global bounds and quasilinear Riccati type equations below the natural exponent (2014, background): “2) in the natural growth case q = p, see for example [1, 4, 5, 12, 13, 16, 28, 29, 35, 36, 43, 44, 45, 49, 57].”
Solvability of Uniformly Elliptic Fully Nonlinear PDE (2010, unknown): “We refer to [BMP1], [BMP2], [AGP] for the case c0 FM ], [GMP] for the case c0 = 0 (see also the references in these works).”
Nonlinear elliptic equations with natural growth in general domains (2002, methodology): “Then we extract a weakly converging subsequence and we try to pass to the limit in the weak formulation of (Pn); in order to do this we need a result of local strong convergence of the gradients, which is proved in Section 4, using a local version of the technique used in [10].”
Some remarks on elliptic problems with critical growth in the gradient (2006, background): “Later on, many authors have been considering elliptic equations with first order terms having quadratic growth with respect to the gradients (see for instance [14], [15], [16], [17], [18], [19], [21], [22], [25], [26], [29], [32], [31], [40], [42], [43], [46], [50] and references therein).”
An elliptic problem with a lower order term having singular behaviour (2009, background): “If 0 k 1, we prove the existence of a solution for both the “+” and the “−” signs, while if k ≥ 1, we prove the existence of a solution for the “+” sign only.”
Singular quasilinear equations with quadratic growth in the gradient without sign condition (2009, unknown): “However, a smallness condition on the function a(x) is imposed in [13,16], while in [11,19] the authors consider a general term a(x) but they impose an asymptotic condition on g(x, s).”