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- University of NottinghamGB17 papers
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5 papers · 1 filter
Damping-Diffusion-Noise Interactions in the Stochastic Camassa-Holm Equation
Diego Alonso-Orán, Peter H. C. Pang, Hao Tang
In this paper we investigate the effects of the interaction between time-inhomogeneous damping, non-local diffusion, and noise on classical solutions to the Camassa-Holm equation i…
Fractional Korn's inequalities without boundary conditions
D. Harutyunyan, T. Mengesha, H. Mikayelyan +1
This work establishes fractional analogues of Korn's first and second inequalities for vector fields in fractional Sobolev spaces defined over a bounded domain. The validity of the…
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…
Constrained optimal rearrangement problem leading to a new type obstacle problem
Hayk Mikayelyan
We consider a new type of obstacle problem in the cylindrical domain arising from minimization of the functional $$ \int_Ω\frac{1}{2}|\nabla u|^2+χ_{\{v>0\}}udx,…
Regularity up to the Crack-Tip for the Mumford-Shah problem
John Andersson, Hayk Mikayelyan
We prove that if is a minimizer of the functional $$ J(u,Γ)=\int_{B_1(0)\setminus Γ}|\nabla u|^2dx +\H^1(Γ) $$ and connects to a point in the interior…