Partial symmetry and asymptotic behavior for some elliptic variational problems

By D. Smets, Michel Willem. 2003

172 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/28864f6551b86d3547287f5ef17ab99095857609

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On the symmetry of minimizers (2007, methodology): “We have to mention that in a series of recent papers (see [2], [15], [17] and references therein), different new techniques were developed to study the symmetry of solutions for some classes of elliptic problems.”
Multiplicity Results for the Supercritical Hénon Equation (2004, background): “Further results on the subcritical Hénon equation (such as symmetry properties of solutions and blow–up profile of ground states) can be found in [1], [3] and [10].”
Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities (2004, background): “Our argument is different from that in [17].”
The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions (2008, background): “In this paper, we focus on the less investigated bidimensional case N = 2, and besides symmetry breaking phenomena, we explore the possibility of ensuring radial symmetry for the extremal ua,b, a property which cannot be handled as in [12,13,16], (see in particular [16, Remark 4.”
Infinitely many nonradial solutions for the Hénon equation with critical growth (2013, background): “The reader can refer to [1], [2], [4], [8], [10], [11], and [14] for results on Hénon equations involving subcritical and near critical exponents.”
Non radial positive solutions for the Hénon equation with critical growth (2005, background): “The reason why this occurs is clearly pointed out in [ 13 ] as follows: for p close to 2 ∗ minimizers tend to “concentrate” about a Non radial solutions for the critical H´ enon equation”
Hamiltonian elliptic systems: a guide to variational frameworks (2014, background): “with respect to the axis Reand nonincreasing in the polar angle = arccos(xe) 2[0;ˇ]. We mention that, up to our knowledge, the link between polarization and foliated Schwarz symmetry appeared rst in [103]; cf. [21, Theorem 2.6] for further results about the foliated Schwarz symmetry of least energy ”
Symmetry of Solutions to Variational Problems for Nonlinear Elliptic Equations via Reflection Methods (2010, methodology): “The strategy of the proofs in [ 77 , 85] is to approximate symmetrization by polarization.”