Projet de Recherche

Qualitative study of nonlinear PDE's

• Maria-Magdalena Boureanu, Vicenţiu Rădulescu - Université de Craiova.
• Olivier Goubet, Benedetta Noris - Université "Jules Verne" de Picardie, Amiens.

• In [1] we have studied existence and regularity of solutions for a class of Robin problems on bounded non-smooth domains, which may include non-Lipschitz domains. Part of the results obtained in [1] was presented at:
  The International Conference on Applied Mathematics and Numerical Methods (ICAMNM, second edition), Craiova, Romania, October 19-20, 2018, with the presentation “Critical point theory applied to nonlinear problem” communicated by M.M. Boureanu.
• In [2] we conduct our study in the framework of the weighted Lebesgue and Sobolev spaces with variable exponent and we establish several properties for the functional associated to our class of systems.
• During her visit at the University of Craiova, Dr. B. Noris has made a scientific presentation at a scientific seminar at University of Craiova, on October 30, 2018:
  “Radial positive solutions for a class of Neumann problems without growth conditions”.
  This presentation is correlated with a new collaboration project started between M.M. Boureanu, O. Goubet and B. Noris, since we intend to adapt some of the results previously obtained by Dr. Noris to other type of operators [3].

1. M.M. Boureanu and A. Velez - Santiago, “Fine regularity for elliptic and parabolic anisotropic Robin problems with variable exponents”, Journal of Differential Equations 266 (12), p. 8164 - 8232, (2019);
2. M.M. Boureanu, V. Radulescu and A. Ribeiro, “Variable exponent elliptic systems involving Leray-Lions type operators”, (in preparation);
3. M.M. Boureanu, O. Goubet and B. Noris, “Radial positive solutions for a class of elliptic problems involving mean curvature operator”, (in preparation).