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On the local boundedness of generalized minimizers of variational problems with linear growth. (English) Zbl 1401.49066
Authors’ abstract: We prove local boundedness of generalized solutions to a large class of variational problems of linear growth including boundary value problems of minimal surface type and models from image analysis related to the procedure of TV regularization occurring in connection with the denoising of images, which might even be coupled with an inpainting process. Our main argument relies on a Moser-type iteration procedure.
MSC:
49Q20 Variational problems in a geometric measure-theoretic setting
49J45 Methods involving semicontinuity and convergence; relaxation
49N60 Regularity of solutions in optimal control
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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