Nonexistence results and estimates for some nonlinear elliptic problems

By Marie-Franccoise Bidaut-V'eron, Stanislav I. Pohozaev. 2001

256 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d3d6ae633213870c26e36048c35c6945385fca67

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Quasilinear and Hessian equations of Lane-Emden type (2005, methodology): “Universal estimates for solutions, Liouville-type theorems, and analysis of removable singularities are due to Bidaut-V´eron, Mitidieri and Pohozaev [BV1]‐[BV3], [ BVP ], [MP], and Serrin and Zou [SZ].”
Singular quasilinear and Hessian equations and inequalities (2009, background): “Quasilinear equations (1.1) in the special case 1 have been studied extensively over the past 20 years (see [5]‐[7], [ 8 ], [9], [30], [36]).”
A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities (2010, methodology): “(W-p-C) The function A is called S-p-C (strongly-p-coercive) (see [57,46,5] for details), if there exist a, b > 0 constants such that ( A (x, t,w) · w) b∣∣wp∣∣ a∣∣A (x, t,w)∣∣p′ for each x ∈ R, t ∈ R, w ∈ R .”
Removable Singularities and Existence for a Quasilinear Equation with Absorption or Source Term and Measure Data (2003, background): “1 These ideas were already used in [10] to obtain upper estimates for more general problems with possible singularities, and also in [9] to study the initial trace problem for a parabolic equation with absorption.”
Towards a Unified Approach to Nonexistence of Solutions for a Class of Differential Inequalities (2004, background): “For additional results the reader may refer to [4],[24],[25], [26],[38],[39],[44] and [45].”
On the connection between two quasilinear elliptic problems with source terms of order 0 or 1 (2008, background): “17, based on regularity results of [10] and Harnack inequality.”
Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle (2010, result): “In two important papers, Bidaut-Veron [6] and Bidaut-Veron and Pohozaev [8] extended these results by dropping the restrictions on the behavior of a supersolution u and by showing that the same results hold in exterior domains of .”