We prove local gradient bounds and interior Hölder estimates for the first derivatives of functions u ∈ W1,loc1(Ω) which locally minimize the variational integral I(u) = ∫Ω f(∇u)dx subject to the side condition Ψ1 ≤ u ≤ Ψ2. We establish these results for various classes of integrands f with non-standard growth. For example, in the case of smooth f the (s,μ,q)-condition is sufficient. A second class consists of all convex functions f with (p,q)-growth. © Heldermann Verlag.

A priori gradient bounds and local C1,α-estimates for (double) obstacle problems under non-standard growth conditions / Bildhauer, M.; Fuchs, M.; Mingione, G.. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 20:4(2001), pp. 959-985.

A priori gradient bounds and local C1,α-estimates for (double) obstacle problems under non-standard growth conditions

Mingione G.
2001

Abstract

We prove local gradient bounds and interior Hölder estimates for the first derivatives of functions u ∈ W1,loc1(Ω) which locally minimize the variational integral I(u) = ∫Ω f(∇u)dx subject to the side condition Ψ1 ≤ u ≤ Ψ2. We establish these results for various classes of integrands f with non-standard growth. For example, in the case of smooth f the (s,μ,q)-condition is sufficient. A second class consists of all convex functions f with (p,q)-growth. © Heldermann Verlag.
A priori gradient bounds and local C1,α-estimates for (double) obstacle problems under non-standard growth conditions / Bildhauer, M.; Fuchs, M.; Mingione, G.. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 20:4(2001), pp. 959-985.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2895060
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