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Continuity results for solutions of certain degenerate parabolic equations

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Continuity results for solutions of certain degenerate parabolic equations RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA GIULIA SARGENTI Continuity results for solutions of certain degenerate parabolic equations Rendiconti del Seminario Matematico della Università di Padova, tome 99 (1998), p. 105-131. <http://www.numdam.org/item?id=RSMUP_1998__99__105_0> © Rendiconti del Seminario Matematico della Università di Padova, 1998, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’ac- cord avec les conditions générales d’utilisation (http://www.numdam.org/legal. php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Continuity Results for Solutions of Certain Degenerate Parabolic Equations. GIULIA SARGENTI(*) ABSTRACT - In this paper we prove the local continuity for essentially bounded local weak solutions of a large class of degenerate parabolic equations, with principal part characterized by non standard growth conditions. 1. - Introduction. The present section is devoted to introduce a class of quasilinear de- generate parabolic equations of the type where = S~ x ( o, T), ,~ is a bounded domain in R N and 0 T 00, 6D’ is the space of distributions on and Du denotes the gradient re- spect only to the space variable. Here we assume: (1.2) F: R x (n, z) - F(n, z) is continuous in n, uniformly continuous In z . There exists two functions C1, C2, such that for all 17 E=- R, (*) Indirizzo dell’A.: Dipartimento di Matematica, Universita di Roma «La Sapienza», Piazzale Aldo Moro 2, 00185 Roma, Italy. E-mail: [email protected] 106 for a.e. (x, t) E Q T. Here

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