5 papers
Harnack inequality for superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar +1
The main aim of this paper is to establish the Hölder continuity and the Harnack inequality for weak solutions to Dirichlet problems associated with superposition operators of mix…
Regularity of superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar +1
We extend the De Giorgi--Nash--Moser theory to superposition operators of mixed fractional operators. In particular, we investigate several regularity properties for this class of…
Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar
This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We esta…
Superlinear problems involving nonlinear superposition operators of mixed fractional order
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar
In this work, we study a class of elliptic problems involving nonlinear superpositions of fractional operators of the form \[ A_{μ,p}u := \int_{[0,1]} (-Î)_{p}^{s} u \, dμ(s), \…
On sign-changing solutions for mixed local and nonlocal -Laplace operator
Souvik Bhowmick, Sekhar Ghosh
In this paper, we use the method of invariant sets of descending flows to demonstrate the existence of multiple sign-changing solutions for a class of elliptic problems with zero D…