We prove the continuity of bounded, weak solutions of the singular parabolic equation β(u)t = Lu, where Lu is a second-order, uniformly elliptic operator in divergence form with bounded and measurable coefficients and β(·) is a maximal monotone graph in R × R exhibiting an arbitrary but finite number of jumps.
Continuity of weak solutions of a singular parabolic equation / U. GIANAZZA; V. VESPRI.. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 8:(2003), pp. 1341-1376.
Continuity of weak solutions of a singular parabolic equation
VESPRI, VINCENZO
2003
Abstract
We prove the continuity of bounded, weak solutions of the singular parabolic equation β(u)t = Lu, where Lu is a second-order, uniformly elliptic operator in divergence form with bounded and measurable coefficients and β(·) is a maximal monotone graph in R × R exhibiting an arbitrary but finite number of jumps.
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