8 citations · 15 across the 18 of their papers we have counts for
19 papers
On the fractional Korn inequality in bounded domains: Counterexamples to the case
Davit Harutyunyan, Hayk Mikayelyan
The validity of Korn's first inequality in the fractional setting in bounded domains has been open. We resolve this problem by proving that in fact Korn's first inequality holds in…
Stabilization technique applied to curve shortening flow in
Hayk Mikayelyan
We apply the stabilization technique, developed by T. Zelenyak in 1960s for parabolic equations, on curve shortening flow in , and derive several new monotonicity formulas. A…
Fractional optimal maximization problem and the unstable fractional obstacle problem
Julian Fernandez Bonder, Zhiwei Cheng, Hayk Mikayelyan
We consider an optimal rearrangement maximization problem involving the fractional Laplace operator , , and the Gagliardo-Nirenberg seminorm . We prove the ex…
Optimal rearrangement problem and normalized obstacle problem in the fractional setting
Julián Fernández Bonder, Zhiwei Cheng, Hayk Mikayelyan
We consider an optimal rearrangement minimization problem involving the fractional Laplace operator , , and Gagliardo-Nirenberg seminorm . We prove the existe…
Stationarity of the crack-front for the Mumford-Shah problem in 3D
Antoine Lemenant, Hayk Mikayelyan
In this paper we exhibit a family of stationary solutions of the Mumford-Shah functional in , arbitrary close to a crack-front. Unlike other examples, known in the li…
Weighted asymptotic Korn and interpolation Korn inequalities with singular weights
Davit Harutyunyan, Hayk Mikayelyan
In this work we derive asymptotically sharp weighted Korn and Korn-like interpolation (or first and a half) inequalities in thin domains with singular weights. The constants (K…