18 citations · 35 across the 6 of their papers we have counts for
7 papers
Γ-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces
Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie +1
We derive Onsager-Machlup functionals for countable product measures on weighted subspaces of the sequence space . Each measure in the product is…
Γ-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems
Birzhan Ayanbayev, Ilja Klebanov, Han Cheng Lie +1
The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a MAP estimator. The MAP estimator essentially coincides with…
On the inverse source identification problem in for fully nonlinear elliptic PDE
Birzhan Ayanbayev, Nikos Katzourakis
In this paper we generalise the results proved in [N. Katzourakis, An regularisation strategy to the inverse source identification problem for elliptic equations, SIAM J…
Vectorial variational principles in and their characterisation through PDE systems
Birzhan Ayanbayev, Nikos Katzourakis
We discuss two distinct minimality principles for general supremal first order functionals for maps and characterise them through solvability of associated second order PDE systems…
Explicit -harmonic functions in high dimensions
Birzhan Ayanbayev
The aim of this work is to derive new explicit solutions to the -Laplace equation, the fundamental PDE arising in Calculus of Variations in the space . These solu…
Rigidity and flatness of the image of certain classes of mappings having tangential Laplacian
Hussien Abugirda, Birzhan Ayanbayev, Nikos Katzourakis
In this paper we consider the PDE system of vanishing normal projection of the Laplacian for maps : \[ [\![\mathrm{D…
A Pointwise Characterisation of the PDE System of Vectorial Calculus of Variations in
Birzhan Ayanbayev, Nikos Katzourakis
Let with open. Given we consider the functional \[ \tag{1} \label{1} E_\infty…