Continuous rearrangement and symmetry of solutions of elliptic problems
By F. Brock. 2000
111 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ebf2c1212a737f01502f2fe84168d22c99153dec
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
- Berardino Sciunzi
- Manuel del Pino
- Lucio Damascelli
- Jean Dolbeault
- Alessio Figalli
- Michael Loss
- Rupert L. Frank
- Zongming Guo
In Computational Theory and Mathematics
- Berardino Sciunzi
- Lucio Damascelli
- Jean Dolbeault
- Manuel del Pino
- Zongming Guo
- Filomena Pacella
- Maria J. Esteban
- Rupert L. Frank
In Mathematical Physics
- Berardino Sciunzi
- Manuel del Pino
- Lucio Damascelli
- Alessio Figalli
- Jean Dolbeault
- Maria J. Esteban
- Rupert L. Frank
- Filomena Pacella
Citations in the corpus
- Large and Small Solutions of a Class of Quasilinear Elliptic Eigenvalue Problems (2002, methodology): “(To obtain the symmetry results, in [20], the author used the results in [3] and [4].”
- Monotonicity and symmetry results for $p$-Laplace equations and applications (2000, background): “Remark 1.2. In the case of the ball Brock [3],[ 4 ] proved the radial”
- Regularity, monotonicity and symmetry of positive solutions of m-Laplace equations (2004, methodology): “Let us finally remark that in the case of ground states of quasilinear elliptic equations in the whole space, radial symmetry results were obtained in [9,22,4,5].”
- Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (2022, methodology): “Brock’s construction, in turn, is based on ideas of Rogers [59] and Brascamp–Lieb–Luttinger [11].”
- The optimal Euclidean Lp-Sobolev logarithmic inequality (2003, methodology): “Identification of all extremals use symmetry results of GidasNi–Nirenberg-type for the p-Laplacian [7,9].”
- Symmetry of Solutions to Variational Problems for Nonlinear Elliptic Equations via Reflection Methods (2010, unknown): “It is stronger than the notion of local symmetry given in other papers of Brock (see [20, 21 ]), which includes functions with superlevel sets given as disjoint unions of balls.”
- Symmetrization and minimax principles (2005, background): “its domain is the union of annuli on which it is radial and of a set on which ∇u = 0 almost everywhere [3].”