L’analyse mathématique des équations aux dérivées partielles est au cœur des recherches effectuées au sein de l’équipe d’analyse. Cela nous conduit à développer de nouvelles méthodes, notamment topologiques ou variationnelles pour démontrer l’existence de solutions, à étudier les espaces de fonctions apparaissant en équations aux dérivées partielles et à démontrer de nouvelles inégalités fonctionnelles, et à analyser les propriétés qualitatives des solutions (régularité, symétrie, comportement asymptotique…).
Membres du groupe
Académiques permanents
- Heiner OLBERMANN
- Augusto PONCE
- Jean VAN SCHAFTINGEN
Professeurs émérites
- Jean MAWHIN
- Michel WILLEM
Post-doctorants
- Adolfo ARROYO RABASA
- Stefano BUCCHERI
- Bohdan BULANYI
Doctorants
- Corentin FRANÇOIS
- Paul UBILLUS
- Benoît VAN VAERENBERGH
Publications représentatives du groupe
Articles
- H. Olbermann, Godunov variables and convex entropy for relativistic fluid dynamics with bulk viscosity. J. Math. Phys. 63 (2022), no. 3, Paper No. 031501, 9 pp.
- H. Brezis, J. Van Schaftingen and P.-L. Yung, A surprising formula for Sobolev norms, Proc. Natl. Acad. Sci. USA 118 (2021), no. 8, e2025254118.
- P. Mironescu and J. Van Schaftingen, Lifting in compact covering spaces for fractional Sobolev mappings, Anal. PDE 14 (2021), no. 6, 1851–1871.
- A. Monteil, R. Rodiac and J. Van Schaftingen, Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold, Arch. Rat. Mech. Anal. 242 (2021), no. 2, 875–935.
- L. Ambrosio, A. C. Ponce and R. Rodiac, Critical weak-Lp differentiability of singular integrals. Rev. Mat. Iberoam. 36 (2020), no. 7, 2033–2072.
- J. Dekeyser and J. Van Schaftingen, Vortex motion for the lake equations, Comm. Math. Phys. 375 (2020), no. 2, 1459–1501.
- P. Gladbach and H. Olbermann, Coarea formulae and chain rules for the Jacobian determinant in fractional Sobolev spaces. J. Funct. Anal. 278 (2020), no. 2, 108312, 21 pp.
- H.-M. Nguyen and J. Van Schaftingen, Characterization of the traces on the boundary of functions in magnetic Sobolev spaces, Adv. Math. 371 (2020), 107246.
- L. Orsina and A. C. Ponce, On the nonexistence of Green's function and failure of the strong maximum principle. J. Math. Pures Appl. (9) 134 (2020), 72–121.
- A. C. Ponce and D. Spector, A boxing inequality for the fractional perimeter. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 20 (2020), no. 1, 107–141.
- A. Szulkin and M. Willem, On some weakly coercive quasilinear problems with forcing. J. Anal. Math. 140 (2020), no. 1, 267–281.
- A. Farina, C. Mercuri and M. Willem, A Liouville theorem for the p-Laplacian and related questions. Calc. Var. Partial Differential Equations 58 (2019), no. 4, Paper No. 153, 13 pp.
- H. Olbermann, On a Γ-limit of Willmore functionals with additional curvature penalization term. SIAM J. Math. Anal. 51 (2019), no. 3, 2599–2632.
- H. Olbermann, On a boundary value problem for conically deformed thin elastic sheets. Anal. PDE 12 (2019), no. 1, 245–258.
- P. Bousquet, A. C. Ponce and J. Van Schaftingen, Strong density for higher order Sobolev spaces into compact manifolds, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 4, 763–817.
Livres
- G. Dinca, J. Mawhin, Brouwer degree—the core of nonlinear analysis. Progress in Nonlinear Differential Equations and their Applications, 95. Birkhäuser/Springer, Cham, 2021
- A. Ponce, Elliptic PDEs, measures and capacities, EMS Tracts in Mathematics, 23, European Mathematical Society (EMS), Zürich, 2016.
- M. Willem, Functional analysis. Fundamentals and applications, Cornerstones, Birkhäuser/Springer, New York, 2013.