Advances in Differential Equations

Continuity of parabolic $Q$-minima under the presence of irregular obstacles

Catarina Petersson

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We study the pointwise continuity of functions satisfying a certain inequality, deducible from parabolic obstacle problems and valid also for parabolic Q-minima. Employing techniques going back to De Giorgi, we give conditions on the obstacles sufficient to imply continuity of the solution. These conditions are formulated as inequalities for the capacities of sub- and super-level sets of the obstacles, and thus also thin obstacles are considered.

Article information

Adv. Differential Equations, Volume 11, Number 12 (2006), 1397-1436.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B65: Smoothness and regularity of solutions 35K65: Degenerate parabolic equations 35K85: Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40]


Petersson, Catarina. Continuity of parabolic $Q$-minima under the presence of irregular obstacles. Adv. Differential Equations 11 (2006), no. 12, 1397--1436.

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