THE BREZIS-NIRENBERG PROBLEM NEAR CRITICALITY IN DIMENSION 3 ?

By Manuel del Pino, Jean Dolbeault, Monica Musso. 2004

73 citations recorded by the source corpus.

We consider the problem of finding positive solutions of u +u +u q = 0 in a bounded, smooth domain in 3 , under zero Dirichlet boundary conditions. Here q is a number close to the critical exponent 5 and 0 5 and q 5 is suciently small.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0fd39fba928bedeb951aac1e186bf25abbe14ed7

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

1. Angela Pistoia
2. Monica Musso
3. Tobias Weth
4. M. Grossi
5. Yuxin Ge
6. Jean Dolbeault
7. I. Flores
8. Jun-cheng Wei

In Computational Theory and Mathematics

1. Angela Pistoia
2. Monica Musso
3. Tobias Weth
4. M. Grossi
5. Yuxin Ge
6. I. Flores
7. Jean Dolbeault
8. Jun-cheng Wei

Citations in the corpus

• Geometry of phase space and solutions of semilinear elliptic equations in a ball (2007, background): “for p − N+2 N−2 > 0, small [10, 12], which also has an ODE interpretation [11].”
• Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains (2010, background): “The result in [29], as well as in other related problems where construction of tower of bubbles is obtained [14, 15, 16, 32], rely strongly on the assumption of symmetry of the domain.”
• Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem (2007, methodology): “Here we decided to include the details, since the expansion shows crucial differences in comparison with [20,21,24].”
• Tower of bubbles for almost critical problems in general domains (2010, background): “Nevertheless, in [6] the case N = 3 is treated.”
• Multiple Blow-Up Phenomena for the Sinh-Poisson Equation (2012, background): “In particular, towers of positive bubbles were found by Del Pino-DolbeaultMusso [6, 7], Ge-Jing-Pacard [15] and Del Pino-Musso-Pistoia [12], while towers of signchanging bubbles were built by Pistoia-Weth [26], Musso-Pistoia [23, 24] and Ge-MussoPistoia [16].”