Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian.
Equality cases in the symmetrization inequalities for Brownian transition functions and Dirichlet heat kernels.
Estimate of the pressure when its gradient is the divergence of a measure. Applications
In this paper, a estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on , or on a regular bounded open set of . The proof is based partially on the Strauss inequality [Strauss,Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc. 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions...
Estimate of the pressure when its gradient is the divergence of a measure. Applications
In this paper, a estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on , or on a regular bounded open set of . The proof is based partially on the Strauss inequality [Strauss, Partial Differential Equations: Proc. Symp. Pure Math.23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc.9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions...
Estimates for derivatives of the Green functions on homogeneous manifolds of negative curvature.
Estimates for the Green function and existence of positive solutions for higher-order elliptic equations.
Estimates for the Green function and singular solutions for polyharmonic nonlinear equation.
Estimates for the parametrix of the Kohn Laplacian on certain domains.
Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms.
Existence and estimates of Green's function for degenerate elliptic equations
Existence of positive solutions for nonlinear boundary value problems in bounded domains of .
Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of .
Existence of positive solutions for some polyharmonic nonlinear equations in .
Existence results for polyharmonic boundary value problems in the unit ball.
Explicit fundamental solutions of some second order differential operators on Heisenberg groups
Let p,q,n be natural numbers such that p+q = n. Let be either ℂ, the complex numbers field, or ℍ, the quaternionic division algebra. We consider the Heisenberg group N(p,q,) defined ⁿ × ℑ , with group law given by (v,ζ)(v’,ζ’) = (v + v’, ζ + ζ’- 1/2 ℑ B(v,v’)), where . Let U(p,q,) be the group of n × n matrices with coefficients in that leave the form B invariant. We compute explicit fundamental solutions of some second order differential operators on N(p,q,) which are canonically associated to...
Explicit solutions of some fractional partial differential equations via stable subordinators.
Exponential decay of averaged Green functions for random Schrödinger operators. A direct approach