We prove the existence of a Radon measure-valued solution for a class of nonlinear degenerate parabolic equations with a "logarithmic diffusion" when the initial datum u (0) is a bounded Radon measure, and we study the regularity of these solutions. In particular, we prove that a regularizing effect appears if the initial datum is diffused with respect to the "C (2)-capacity" since in this case the solution becomes a summable function. Finally, we study the uniqueness of these measure-valued solutions.

Measure-valued solutions of nonlinear parabolic equations with "logarithmic diffusion" / Orsina, Luigi; Porzio, Maria Michaela; F., Smarrazzo. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - STAMPA. - 15:(2015), pp. 609-645. [10.1007/s00028-015-0275-5]

Measure-valued solutions of nonlinear parabolic equations with "logarithmic diffusion"

ORSINA, Luigi;PORZIO, Maria Michaela;
2015

Abstract

We prove the existence of a Radon measure-valued solution for a class of nonlinear degenerate parabolic equations with a "logarithmic diffusion" when the initial datum u (0) is a bounded Radon measure, and we study the regularity of these solutions. In particular, we prove that a regularizing effect appears if the initial datum is diffused with respect to the "C (2)-capacity" since in this case the solution becomes a summable function. Finally, we study the uniqueness of these measure-valued solutions.
2015
Radon measures; nonlinear degenerate parabolic equations; existence and uniqueness results
01 Pubblicazione su rivista::01a Articolo in rivista
Measure-valued solutions of nonlinear parabolic equations with "logarithmic diffusion" / Orsina, Luigi; Porzio, Maria Michaela; F., Smarrazzo. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - STAMPA. - 15:(2015), pp. 609-645. [10.1007/s00028-015-0275-5]
File allegati a questo prodotto
File Dimensione Formato  
Orsina_Measure-valued-solutions_2015.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 752.9 kB
Formato Adobe PDF
752.9 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/783083
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 8
social impact