Nonlinear elliptic equations with natural growth in general domains

By Andrea Dall'Aglio, Daniela Giachetti, Jean-Pierre Puel. 2002

56 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/bbd23fe878aff58b27b7bfae672849de84f3da09

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Alessio Porretta

Citations in the corpus

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.”
Partial Differential Equations Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms (2006, background): “When q = 2, condition (4) becomes f ∈ LN/2(Ω); in this case existence of a solution of (1) which satisfies the further regularity eγ |u| − 1 ∈ H 1 0 (Ω) has been proved in [10] if α0 = 0 and in [ 8 ] if α0 > 0 (previous references for the case where q = 2 and m>N /2 are, e.g., [4,5]).”
Solvability of Uniformly Elliptic Fully Nonlinear PDE (2010, unknown): “We refer to [BMP1], [BMP2], [ AGP ] for the case c0 < 0, and to [MPS], [FM], [GMP] for the case c0 = 0 (see also the references in these works).”
Dirichlet problems with singular and gradient quadratic lower order terms (2008, background): “Puel [14–16] (see also [7,19,20]), where we proved existence of bounded solutions (without the assumption g(x, s, ξ) s ≥ 0 and with the assumption f ∈ L(Ω), m > N/2).”
Uniqueness for unbounded solutions to stationary viscous Hamilton-Jacobi equations (2006, unknown): “s for the case q= 2 can be found in several works, among which we recall the series of papers by L. Boccardo, F. Murat, J.P. Puel (see e.g. [8], [9]) and more recently, assuming fin LN2 (Ω), in [13], [10]. Under assumption (1.4) with 1 < q < 2, the existence of a solution for problems as (1.2)”