Existence results for nonlinear elliptic equations with degenerate coercivity

By A. Alvino, Lucio Boccardo, V. Ferone, Luigi Orsina, G. Trombetti. 2003

198 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/64cac7525bba12d8b0c73b1ad7e550c869912b8e

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Symmetrization in Anisotropic Elliptic Problems (2007, methodology): “1 will reveal that the same argument applies also to solutions from this class, whenever f (·, 0) is just in L 1 (Ω) (see also Alvino et al, 2000 2003 for applications of symmetrization techniques to entropy solutions).”
THE REGULARIZING EFFECTS OF SOME LOWER ORDER TERMS IN AN ELLIPTIC EQUATION WITH DEGENERATE COERCIVITY (2010, background): “6) may have no solution at all, even if the datum f is a constant function (see [7] and [1]).”
Existence and regularity results for some parabolic equations with degenerate coercivity (2012, background): “2) is 1 + 2 N , but 1 for elliptic equations (see [1, 2, 9, 10, 13, 18, 19]).”
The obstacle problem for nonlinear elliptic equations with variable growth and L1-data (2008, methodology): “The result builds upon [8] and [4], assumes the exponent to be log-Hölder continuous, and relies on a priori estimates in Marcinkiewicz spaces with variable exponent.”
UNIQUENESS OF SOLUTIONS FOR SOME ELLIPTIC EQUATIONS WITH A QUADRATIC GRADIENT TERM (2010, background): “On the other hand, (nonsingular) elliptic equations having a principal term with degenerate coercivity have been studied in the nineties (see [2,19] and references therein).”
On the connection between two quasilinear elliptic problems with source terms of order 0 or 1 (2008, background): “It improves the results of [11], [38], [4], [19] and extends the estimates of the gradient given in [46], [47] for solutions U ∈ W 1,p 0 (Ω).”
Boundedness of the extremal solution of some p-Laplacian problems (2007, background): “The following result can be found in [13] or in [1].”
Nonlinear elliptic equations having a gradient term with natural growth (2006, background): “1 Note that assumption (A2) includes the case of a non uniformly coercive operator, as considered for instance in [3] or [1].”