Fundamental Solutions and Two Properties of Elliptic Maximal and Minimal Operators

  title={Fundamental Solutions and Two Properties of Elliptic Maximal and Minimal Operators},
  author={Patricio Felmer and Alexander M Quaas},
For a large class of nonlinear second order elliptic differential operators, we define a concept of dimension, upon which we construct a fundamental solution. This allows us to prove two properties associated to these operators, which are generalizations of properties for the Laplacian and Pucci’s operators. If M denotes such an operator, the first property deals with the possibility of removing singularities of solutions to the equation M(Du)− u = 0, in B \ {0}, where B is a ball in RN . The… CONTINUE READING
6 Citations
28 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 28 references

On the Liouville property for fully nonlinear equations, Ann

  • A. Cutri, F. Leoni
  • Inst. H. Poincaré Analyse Non Linéaire
  • 2001
Highly Influential
7 Excerpts

Symmetry properties and isolated singularities of positive solutions of nonlinear elliptic equations. Nonlinear partial differential equations in engineering and applied science

  • B. Gidas
  • (Proc. Conf.,
  • 1979
Highly Influential
9 Excerpts

Singularities of solutions of second order quasilinear equations. Pitman Research Notes in Mathematics Series, 353

  • L. Véron
  • Avda. España 1680,
  • 1996
Highly Influential
7 Excerpts

Fully Nonlinear Elliptic Equations, American Mathematical Society

  • X. Cabré, L. Caffarelli
  • Colloquium Publication,
  • 1995
Highly Influential
5 Excerpts

Critical Exponents for Uniformly Elliptic Extremal Operators

  • P. Felmer, A. Quaas
  • Indiana Univ. Math. J
  • 2006
Highly Influential
3 Excerpts

Viscosity solutions of fully nonlinear second-order elliptic partial differential equations

  • P. L. Lions, H. Ishi
  • Journal of Differential Equations
  • 1990
Highly Influential
3 Excerpts

Global and local behavior of positive solutions of nonlinear elliptic equations

  • B. Gidas, J. Spruck
  • Comm. Pure Appl. Math
  • 1981
Highly Influential
4 Excerpts

Similar Papers

Loading similar papers…