4 citations · 20 across the 44 of their papers we have counts for
6 papers · 2 filters
On -eigenvalues of the weighted -Laplace operator in outward Hölder cuspidal domains
Prashanta Garain, Valerii Pchelintsev, Alexander Ukhlov
In this paper, we will study Neumann -eigenvalue problem for the weighted -Laplace operator in outward Hölder cuspidal domains. The suggested method is based on the compo…
Higher Hölder regularity for the fractional -Laplace equation in the subquadratic case
Prashanta Garain, Erik Lindgren
We study the fractional -Laplace equation for and in the subquadratic case . We provide Hölder estimates with an explicit Hölder exponent. Th…
On the regularity theory for mixed anisotropic and nonlocal -Laplace equations and its applications to singular problems
Prashanta Garain, Wontae Kim, Juha Kinnunen
We establish existence results for a class of mixed anisotropic and nonlocal -Laplace equation with singular nonlinearities. We consider both constant and variable singular expo…
Mixed local and nonlocal Dirichlet -eigenvalue problem
Prashanta Garain, Alexander Ukhlov
In this article, we consider the spectral problem for the mixed local and nonlocal -Laplace operator. We discuss the existence and regularity of eigenfunction of the associated…
On the Neumann -eigenvalue problem in Hölder singular domains
Prashanta Garain, Valerii Pchelintsev, Alexander Ukhlov
In the article we study the Neumann -eigenvalue problems in bounded Hölder -singular domains . In the case and we prov…
On a class of mixed local and nonlocal semilinear elliptic equation with singular nonlinearity
Prashanta Garain
In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish existence of at least one weak…