16 papers
Mixed local and nonlocal weighted singular quasilinear elliptic problem and its associated Sobolev-type inequality
Prashanta Garain
We consider a class of mixed anisotropic and nonlocal singular quasilinear elliptic problem associated with Muckenhoupt weights. The presence of the singular nonlinearity, which bl…
On the regularity theory for mixed local and nonlocal weighted quasilinear elliptic equations
Sanjit Biswas, Prashanta Garain
We investigate a broad class of mixed local and nonlocal degenerate -Laplace equations with general right-hand sides. The degeneracy is governed by Muckenhoupt -weights, yi…
Two alternative proofs of weak Harnack inequality for mixed local and nonlocal -Laplace equations with a nonhomogeneity
Prashanta Garain
We study a class of mixed local and nonlocal -Laplace equations with prototype \[ -Î_p u + (-Î_p)^s u = f \quad \text{in } Ω, \] where is bounded and…
Ground state solutions of mixed local-nonlolcal equations with Hartree type nonlinearities
Gurdev Chand Anthal, Prashanta Garain, Nidhi Nidhi
We study a class of mixed local-nonlocal equations with Hartree-type nonlinearities of the form \begin{equation}\label{meqnab} -Îu + (-Î)^s u + u = (I_α* F(u))\,F'(u) \quad \tex…
On mixed local-nonlocal Sobolev-type inequalities and their connection with singular equations in the Heisenberg group
Prashanta Garain
In this work, we establish a mixed local--nonlocal Sobolev-type inequality in the Heisenberg group and demonstrate that its extremals coincide with solutions to the corresponding m…
Mixed local-nonlocal -Laplace equation with variable singular nonlinearity in the Heisenberg group
Prashanta Garain
We investigate a mixed local-nonlocal -Laplace equation on the Heisenberg group, where the nonlinear term features a variable singular exponent. Our analysis establishes the exi…