Harnack inequality and Liouville properties for L-harmonic operator

Monotonicity of Harnack Inequality for Positive Invariant Harmonic Functions

Boundary Harnack principle and elliptic Harnack inequality

We prove a scale-invariant boundary Harnack principle for inner uniform domains over a large family of Dirichlet spaces. A novel feature of our work is that our assumptions are robust to time changes of the corresponding diffusions. In particular, we do not assume volume doubling property for the symmetric measure.

Boundary Harnack Inequality for Α-harmonic Functions on the Sierpiński Triangle

The analysis and probability theory on fractals underwent rapid development in last twenty years, see [1, 11, 27, 28] and the references therein. Diffusion processes were constructed for the Sierpiński triangle [4, 15, 21] and more generally for some simple nested fractals [17] and Sierpiński carpets [2, 18, 20, 22]. In [25] Stós introduced a class of subordinate processes on d-sets, called α-s...

On Generalization of Sturm-Liouville Theory for Fractional Bessel Operator

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

Maximum principles, Harnack inequality for classical solutions

where the matrix (aij) is symmetric, and uniformly elliptic (aij) ≥ γI, for some γ > 0. In terms of regularity of the coefficients, let us assume the are continuous functions. As opposed to the interior and boundary regularity estimates, where we worked with integral quantities, here we work with pointwise estimates on the solution. The point is the following: assume u ∈ C2(Ω) attains a maximum...