8 citations · 9 across the 12 of their papers we have counts for
8 papers · 1 filter
Critical Sobolev Inequalities and Extremals for a Partially Fractional Grushin Operator
S. Malhotra, L. Sharma, K. Sreenadh
We study the partially fractional Grushin-type operator \begin{equation} \mathcal L_{α,β}u=(-Δ_x)^αu-(1+β)^2|x|^{2β}Δ_y u, \qquad (x,y)\in\mathbb{R}^n\times\mathbb{R}^m,\quad 0<α<1…
A sharp eigenvalue theorem for mixed elliptic problems under mixed boundary conditions
Giovanni Molica Bisci, Lovelesh Sharma
In this paper, we study a class of eigenvalue problems involving both local and nonlocal operators, namely the classical Laplacian and the fractional Laplacian, under mixed boundar…
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…
Normalized solutions to an exponential growth Choquard equation driven by mixed local-nonlocal operator in
Nidhi Nidhi, L. Sharma, K. Sreenadh
In this paper, we study the existence of normalized solutions to the mixed nonlinear Choquard equation with exponential growth \begin{equation} \left\{ \mathcal{L}u+λu = Λ(I_α*F(u)…
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…
The role of the mean curvature in nonlinear p-Laplacian problems with critical exponent
Hichem Chtioui, Hichem Hajaiej, Lovelesh Sharma
We deal with critical nonlinear problems involving the p-Laplacian operator on bounded domains with mixed boundary conditions. We prove the existence of least energy solutions. Our…
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…