Brunn-Minkowski Inequality for p-Harmonic Measures
We prove a local Brunn-Minkowski inequality for a functional corresponding to p-harmonic measures for 2 < p < n+1.
math.AP↗
arXiv subjects
Shirsho Mukherjee
Publications and source records attributed to Shirsho Mukherjee.
On the Minkowski problem for p-harmonic measures
We study the Minkowski problem corresponding to the p-harmonic measures and obtain results previously known for harmonic measures due to Jerison. We show that a class of Borel measures on spheres can be prescribed by p-harmonic measures on convex domains.
math.AP↗
Comparison principles for degenerate sub-elliptic equations in non-divergence form
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 the normalized p-Laplacian. The equations are defined by a collection of vector fields satisfying Hörmander's rank condition and are left invariant with respect to a nilpotent Lie Group.
math.AP↗
Regularity of quasi-linear equations with Hörmander vector fields of step two
If the smooth vector fields $X_1,\ldots,X_m$ and their commutators span the tangent space at every point in $Ω\subseteq \mathbb{R}^N$ for any fixed $m\leq N$, then we establish the full interior regularity theory of quasi-linear equations $\sum_{i=1}^m X_i^*A_i(X_1u, \ldots,X_mu)= 0$ with $p$-Laplacian type growth condition. In other words, we show that a weak solution of the equation is locally $C^{1,α}$.
math.AP↗
Regularity of inhomogeneous Quasi-linear equations on the Heisenberg Group
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.AP↗
A Variational Characterisation of the Second Eigenvalue of the p-Laplacian on Quasi Open Sets
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. This leads also to an existence theorem for spectral functionals depending on the first two eigenvalues of the p-Laplacian.
math.AP↗
On Local Lipschitz Regularity For Quasilinear equations in the Heisenberg Group
The goal of this article is to establish local Lipschitz continuity of weak solutions for a class of degenerated elliptic equations of divergence form, in the Heisenberg Group. The considered hypothesis for the growth and ellipticity condition is a natural generalization of the p-Laplace equation and more general quasilinear elliptic equations with polynomial or exponential type growth.
math.AP↗
$C^{1,α}$-Regularity for variational problems in the Heisenberg group
We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group and prove the Hölder continuity of horizontal gradient of minima.
math.AP↗