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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 1
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Research Article

An existence result for optimal control of singular constraints involving 1-Laplacian operator

Pages 159-167 | Received 16 Nov 2020, Accepted 16 Jun 2021, Published online: 30 Jun 2021
 

Abstract

Learning-based partial differential equations (PDEs), which arise from applications in image processing and computer vision, are optimal control problems governed by PDEs. In this paper, we show the maximal monotonicity of the sum operator of the p-Laplacian and the singular 1-Laplacian. The effective domain of the sum operator is shown to be dense in Hilbert space L2(Ω) equipped with the norm topology. As an application, we derive the existence of optimal solutions to optimal control of singular PDEs involving the sum operator of the p-Laplacian and 1-Laplacian in the continuous setting.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

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