Nonlinear Analysis of PDE


The Nonlinear Analysis is one of the areas of Mathematics that has presented greater growth in the last years due to the fact that the methods developed there are adaptable to many others areas of Mathematics and to different types of Partial Differential Equations. These methods constitute a powerful tool to understand and to solve diverse problems coming from models in Biology, Finance and Control Theory.

Our group has special interest in studying fully nonlinear local and nonlocal elliptic and parabolic equations, which does not prevent us from dealing with problems that involve only the Laplace operator.
We are interested in proving existence and obtaining qualitative properties of the solutions for these types of equations. We have also a special interest in understanding the complexity of the solution sets that these equations sometimes hide. Notice that most of the qualitative properties and the structure of the solution sets that we are searching for will give rise to different interpretations from the theoretical and the applied point of views.

Members

  

Publications

  1. Quaas A, Xia A. Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions. Zeitschrift f{"u}r angewandte Mathematik und Physik 2016;67(3):1-21. [Digital version] [Bibtex]
  2. Quaas A, Xia A. A Liouville type theorem for Lane–Emden systems involving the fractional Laplacian. Nonlinearity 2016;29(8):2279. [Digital version] [Bibtex]
  3. Quaas A, García-Melián J, Alarcón S. Optimal Liouville theorems for supersolutions of elliptic equations with the Laplacian. Annali della Scuola Normale Superiore di Pisa. Classe di scienze 2016;16(1):129-158. [Digital version] [Bibtex]
  4. Quaas A, García-Melián J, Sirakov B. Elliptic equations with absorption in a half-space. Bulletin of the Brazilian Mathematical Society, New Series 2016:1-11. [Digital version] [Bibtex]
  5. Quaas A, Burgos-Pérez M. Á, García-Melián J. Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems. Discrete and Continuous Dynamical Systems 2016;36(9):4703-4721. [Digital version] [Bibtex]
  

Projects

  1. FONDECYT 1151180: Some Nonlinear local and non-local equations
  2. Millennium Nucleus Center for Analysis of PDE, NC130017
  3. CONCURSO “ATRACCIÓN DE CAPITAL HUMANO AVANZADO DEL EXTRANJERO” - Modalidad Estadías Cortas (MEC) –Consolidación de la línea de EDP's en el Doctorado Regional en Matemática
  4. MEC 80140118. Métodos Numéricos y Aplicaciones en el Doctorado Regional de Valparaíso.
  5. Mathamsud 13MATH-03 - QUESP - Quasilinear Equations and Singular Problems
  6. FONDECYT N° 1131135: A GEOMETRIC APPROACH TO SEMILINEAR ELLIPTIC PROBLEMS
  7. FONDECYT 1120842: Multiplicity of solutions for quasilinear and non-local elliptic problems
  8. Ministerio de Ciencia e Innovación - Ministerio de Economía y Competitividad (Gobierno de España) MTM2011-27998 "Propiedades cualitativas de ecuaciones y sistemas elípticos no lineales: difusión local y no local"
  9. FONDECYT N 1110210: Some basic results for local and nonlocal fully nonlinear equations
  10. FONDECYT Nº 1090518: Radial Solutions of Semilinear Elliptic Problems: A Geometric Approach
  11. FONDECYT Nº 1050968: Geometry of Phase Space and Radial Solutions of NonlInear Elliptic Problems
  12. FONDECYT-Postdoctorado Nº 3010044: Geometry of Phase Space and Radial Solutions of Nonlinear Elliptic Problems
  13. FONDECYT POSTDOCTORADO 3150100: LOCAL AND NONLOCAL ELLIPTIC EQUATIONS: WELL-POSEDNESS, REGULARITY AND APPLICATIONS
  14. FONDECYT 3060061: Generalized quasilinear elliptic equations with singular weights.
  15. FONDECYT 11080203: Perturbed quasilinear and semilinear elliptic equations.
  16. FONDECYT N° 11110482: On Qualitative Aspects of some nonlinear elliptic differential equations
  17. ECOS-CONICYT C05E09: Maximal operators, Fourth Order Equations and Quantum Drift-Diffusion
  18. ECOS-CONICYT C02E08: Singular limits and elliptic equations
  19. MathAmSud NAPDE : Nonlinear Analysis and Partial Differential Equations
  20. Fondecyt 1040794: NONLINEAR ELLIPTIC AND PARABOLIC EQUATIONS: NON-DIVERGENCE FORM OPERATORS AND QUALITATIVE PROPERTIES
  21. Fondecyt 1070264: NON PROPER FULLY NONLINEAR ELLIPTIC EQUATION
  22. CONICYT Anillo Act 125 : Center for Analisys of partial differential equations (CAPDE)
  

Theses


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