4 citations · 20 across the 44 of their papers we have counts for
12 papers · 2 filters
On a class of weighted anisotropic -Laplace equation with singular nonlinearity
Prashanta Garain
We consider a class of singular weighted anisotropic -Laplace equations. We provide sufficient condition on the weight function that may vanish or blow up near the origin to ens…
Singular subelliptic equations and Sobolev inequalities on nilpotent Lie groups
Prashanta Garain, Alexander Ukhlov
In this article we study singular subelliptic -Laplace equations and best constants in Sobolev inequalities on nilpotent Lie groups. We prove solvability of these subelliptic $p…
On -eigenvalues of subelliptic operators on nilpotent Lie groups
Prashanta Garain, Alexander Ukhlov
In the article we study the Dirichlet -eigenvalue problem for subelliptic non-commutative operators on nilpotent Lie groups. We prove solvability of this eigenvalue problem…
On the regularity and existence of weak solutions for a class of degenerate singular elliptic problem
Prashanta Garain
In this article, we consider a class of degenerate singular problems. The degeneracy is captured by the presence of a class of -admissible weights, which may vanish or blow up n…
On the regularity theory for mixed local and nonlocal quasilinear parabolic equations
Prashanta Garain, Juha Kinnunen
We consider mixed local and nonlocal quasilinear parabolic equations of -Laplace type and discuss several regularity properties of weak solutions for such equations. More precis…
Weighted anisotropic Sobolev inequality with extremal and associated singular problems
Kaushik Bal, Prashanta Garain
For a given Finsler-Minkowski norm in and a bounded smooth domain , we establish the following weighted aniso…
Multiple solutions for a class of quasilinear problems with double criticality
Karima Ait-Mahiout, Claudianor O. Alves, Prashanta Garain
We establish multiplicity results for the following class of quasilinear problems $$ \left\{ \begin{array}{l} -Δ_Φu=f(x,u) \quad \mbox{in} \quad Ω, \\ u=0 \quad \mbox{on} \quad \pa…
Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems
Prashanta Garain, Alexander Ukhlov
In this article, we consider mixed local and nonlocal Sobolev -inequalities with extremal in the case . We prove that the extremal of such inequalities is un…
Weak Harnack inequality for a mixed local and nonlocal parabolic equation
Prashanta Garain, Juha Kinnunen
This article proves a weak Harnack inequality with a tail term for sign changing supersolutions of a mixed local and nonlocal parabolic equation. Our argument is purely analytic. I…
On an anisotropic p-Laplace equation with variable singular exponent
Kaushik Bal, Prashanta Garain, Tuhina Mukherjee
In this article, we study the following anisotropic p-Laplacian equation with variable exponent given by \begin{equation*} (P)\left\{\begin{split} -Δ_{H,p}u&=\frac{\la f(x)}{u^{q(x…
On the regularity theory for mixed local and nonlocal quasilinear elliptic equations
Prashanta Garain, Juha Kinnunen
We consider a combination of local and nonlocal -Laplace equations and discuss several regularity properties of weak solutions. More precisely, we establish local boundedness of…
Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic -Laplace equations
Agnid Banerjee, Prashanta Garain, Juha Kinnunen
We discuss pointwise behavior of weak supersolutions for a class of doubly nonlinear parabolic fractional -Laplace equations which includes the fractional parabolic -Laplace…