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4 papers · 2 filters
On a coupled PDE model for image restoration
V. B. Surya Prasath, Dmitry Vorotnikov
In this paper, we consider a new coupled PDE model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is sho…
Local and global behaviour of nonlinear equations with natural growth terms
Benjamin J. Jaye, Igor E. Verbitsky
This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumpti…
The Kato Square Root Problem on Submanifolds
Andrew J. Morris
We solve the Kato square root problem for divergence form operators on complete Riemannian manifolds that are embedded in Euclidean space with a bounded second fundamental form. We…
Existence and regularity of positive solutions to elliptic equations of Schrödinger type
Benjamin J. Jaye, Vladimir G. Maz'ya, Igor E. Verbitsky
We prove the existence of positive solutions with optimal local regularity to homogeneous elliptic equations of Schrödinger type, under only a form boundedness assumption on $σ\in…