$H^1$ Solutions of a class of fourth order nonlinear equations for image processing | Zendy

Andrea L. Bertozzi | Zendy; John B. Greer | Zendy

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$H^1$ Solutions of a class of fourth order nonlinear equations for image processing

Author(s) -

Andrea L. Bertozzi,

John B. Greer

Publication year - 2003

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2004.10.349

Subject(s) - nabla symbol , uniqueness , hessian matrix , ode , nonlinear system , operator (biology) , pure mathematics , order (exchange) , sigma , mathematics , sobolev space , class (philosophy) , mathematical physics , mathematical analysis , physics , computer science , omega , quantum mechanics , biochemistry , chemistry , finance , repressor , artificial intelligence , transcription factor , economics , gene

Recently fourth order equations of the form u t = r((G(Ju))ru)have been proposed for noise reduction and simplication of two dimensionalimages. The operator G is a nonlinear functional involving the gradient orHessian of its argument, with decay in the fareld. The operator J is a standardmollier. Using ODE methods on Sobolev spaces, we prove existence anduniqueness of solutions of this problem for Hinitial data.

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