4 citations · 20 across the 44 of their papers we have counts for
9 papers · 1 filter
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…
Gradient higher integrability of bounded solutions to parabolic double-phase systems
Iwona Chlebicka, Prashanta Garain, Wontae Kim
We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon \[u_t-\dv(|\na u|^{p-2}\na u+a(x,t)|\na u|^{q-2}\na u)=-\dv(|F|^{p-2}F+a(x,t)|F|^{q-2}F)\…
Higher Hölder regularity for fractional -Laplace equations
Prashanta Garain, Erik Lindgren
We study the fractional -Laplace equation for and . We establish Hölder estimates with an explicit exponent.…
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 \[ -Δ_p u + (-Δ_p)^s u = f \quad \text{in } Ω, \] where is bounded and ope…
Nonlocal singular problem and associated Sobolev type inequality with extremal in the Heisenberg group
Prashanta Garain
We study a fractional -Laplace equation involving a variable exponent singular nonlinearity in the framework of the Heisenberg group. We first establish the existence and regula…
Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures
Sanjit Biswas, Prashanta Garain
This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatmen…
Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications
Gurdev Chand Anthal, Prashanta Garain
In this article, we establish Pohozaev-type identities for a class of quasilinear elliptic equations and systems involving both local and nonlocal -Laplace operators. Specifical…
Estimates of variational eigenvalues on metric measure spaces
Prashanta Garain, Alexander Ukhlov
In the article, we study variational eigenvalues on doubling metric measure spaces. We prove existence of minimizers of variational Neumann -eigenvalues on metric measure sp…