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Research Institute in Mathematics and Physics

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Research Institute in Mathematics and Physics

Mathematical analysis team

irmp | Louvain-la-Neuve

The differential equations and calculus of variations is at the heart of the research carried out within the analysis team which develop new methods, notably topological or variational, to prove the existence of solutions, to study the spaces of functions appearing in partial differential equations, to obtain new functional inequalities and to analyze the qualitative properties of the solutions Regularity, symmetry, asymptotic behavior…).

Faculty

  • Heiner OLBERMANN
  • Augusto PONCE
  • Jean VAN SCHAFTINGEN

Emeritus

  • Jean MAWHIN
  • Michel WILLEM 

Post-doctoral researchers

  • Adolfo ARROYO RABASA
  • Stefano BUCCHERI
  • Bohdan BULANYI

PhD students

  • Corentin FRANÇOIS
  • Paul UBILLUS
  • Benoît VAN VAERENBERGH

Articles

  • L. Orsina and A. Ponce, Strong maximum principle for Schrödinger operators with singular potential. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 2, 477–493.
  • P. Bousquet, A. 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.
  • V. Moroz and J. Van Schaftingen, Semi-classical states for the Choquard equations, Calc. Var. Partial Differential Equations, 52 (2015), no. 1, 199−235.
  • Z.-Q. Wang and M. Willem, Partial symmetry of vector solutions for elliptic systems, J. Anal. Math. 122 (2014), 69–85.
  • J. Van Schaftingen, Limiting Sobolev inequalities for vector fields and canceling linear differential operators, J. Eur. Math. Soc. (JEMS), 15 (2013), no. 3, 877–921.
  • A. Ponce, Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates, Indiana Univ. Math. J. 62 (2013), 1055–1074
  • T. Bartsch and M. Willem, Some critical minimization problems for functions of bounded variations, J. Funct. Anal. 259 (2010), no. 11, 3025–3035.

Books

  • 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.