8 papers · 1 filter
Hölder regularity and Harnack inequality for the logarithmic Laplacian
Anup Biswas, Subhajit Roy, Aniket Sen +1
In this article, we establish Schauder-type estimates for the logarithmic Laplacian. We show that for a -Hölder inhomogeneous term, the solution is also -Hölder in the interi…
On Coron problems with Choquard term and mixed operator
Jacques Giacomoni, Tuhina Mukherjee, Lovelesh Sharma
In this article, we study a Coron-type problem involving a critical Choquard nonlinearity driven by a mixed operator combining the Laplacian and fractional Laplacian. In annular-ty…
Spectrum properties of mixed operators under the mixed boundary conditions
Lovelesh Sharma
In this paper, we describe the spectrum properties of mixed operators, precisely the superposition of the classical Laplace operator and the fractional Laplace operator in the pres…
The effect of boundary geometry in nonlocal critical problems with Hardy-Littlewood-Sobolev exponent
Hichem Chtioui, Tuhina Mukherjee, Lovelesh Sharma
In this paper we consider a mixed Dirichlet-Neumann boundary value problem. lem involving Choquard nonlinearity with upper critical exponent in the sense of Hardy- Littlewood Sobol…
On singular problems associated with mixed operators under mixed boundary conditions
Tuhina Mukherjee, Lovelesh Sharma
In this paper, we study the following singular problem associated with mixed operators (the combination of the classical Laplace operator and the fractional Laplace operator) under…
On elliptic problems with mixed operators and Dirichlet-Neumann boundary conditions
Tuhina Mukherjee, Lovelesh Sharma
In this paper, we study the existence, nonexistence and multiplicity of positive solutions to the problem given by \begin{equation*} \label{1} \left\{\begin{split} \mathcal{L}u\: &…