## Research Output

Now showing 1 - 4 of 4
• Publication
Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls
(Springer, 2014-07-24)
We study the existence and non-existence of positive singular solutions of second-order non-divergence type elliptic inequalities of the form $\sum\limits_{i,j = 1}^N {a_{ij} (x)\frac{{\partial ^2 u}} {{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^N {b_i (x)\frac{{\partial u}} {{\partial x_i }} \geqslant K(x)u^p ,} - \infty < p - \infty ,$ with measurable coefficients in a punctured ball B R \{0} of ℝ N , N ≥ 1. We prove the existence of a critical value p* which separates the existence region from the non-existence region. We show that in the critical case p = p*, the existence of a singular solution depends on the rate at which the coefficients (a i j ) and (b i ) stabilize at zero, and we provide some optimal conditions in this setting.
• Publication
Analytic content and the isoperimetric inequality in higher dimensions
(Elsevier, 2018-11-01)
This paper establishes a conjecture of Gustafsson and Khavinson, which relates the analytic content of a smoothly bounded domain in RN to the classical isoperimetric inequality. The proof is based on a novel combination of partial balayage with optimal transport theory.
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• Publication
On a class of singular elliptic systems
(Elsevier, 2015-06)
We study the semilinear elliptic system... where Ω⊂R^N(N≥1) is a smooth and bounded domain, p,q,r,s>0. Under suitable ranges of exponents we obtain various results regarding the well posedness of our system.