One of the methods proposed for the study of the problems with a free discontinuity set in two variables has been considered here under slightly different abstract assumptions from those in the previous papers. The technical difficulties are in this new setting simplified and less background is required to the reader. Moreover, applications to problems in several variables can be found thanks to a Sobolev-type theorem which ensures the Holder continuity of certain functions out of a suitable neighborhood of their discontinuity set. Many of the results established so far for the case of two dimensions can be so extended to the general case. A new property is also proved.

Simplified excision techniques for free discontinuity problems in several variables / Solimini, Sergio Fausto. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 151:1(1997), pp. 1-34. [10.1006/jfan.1996.3081]

Simplified excision techniques for free discontinuity problems in several variables

Solimini, Sergio Fausto
1997-01-01

Abstract

One of the methods proposed for the study of the problems with a free discontinuity set in two variables has been considered here under slightly different abstract assumptions from those in the previous papers. The technical difficulties are in this new setting simplified and less background is required to the reader. Moreover, applications to problems in several variables can be found thanks to a Sobolev-type theorem which ensures the Holder continuity of certain functions out of a suitable neighborhood of their discontinuity set. Many of the results established so far for the case of two dimensions can be so extended to the general case. A new property is also proved.
1997
Simplified excision techniques for free discontinuity problems in several variables / Solimini, Sergio Fausto. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 151:1(1997), pp. 1-34. [10.1006/jfan.1996.3081]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/10214
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