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math.AP2024
Comparison principles for degenerate sub-elliptic equations in non-divergence form
Juan J. Manfredi, Shirsho Mukherjee
We prove the comparison principle for viscosity sub/super-solutions of degenerate subelliptic equations in non-divergence form that include the sub-elliptic infinity Laplacian and…
math.AP2019
Regularity of inhomogeneous Quasi-linear equations on the Heisenberg Group
Shirsho Mukherjee, Yannick Sire
We establish Holder continuity of the horizontal gradient of weak solutions to quasi-linear p-Laplacian type non-homogeneous equations in the Heisenberg Group.
math.AP2018
A Variational Characterisation of the Second Eigenvalue of the p-Laplacian on Quasi Open Sets
Nicola Fusco, Shirsho Mukherjee, Yi Ru-Ya Zhang
In this article, we prove a minimax characterization of the second eigenvalue of the p-Laplacian operator on p-quasi-open sets, using a construction based on minimizing movements.…