Convex Variational Problems: Linear, nearly Linear and Anisotropic Growth Conditions

By Michael Bildhauer. 2003

129 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/771371d5b43a9967892002701c3047ec5478c940

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Citations in the corpus

Nonlinear elliptic systems with general growth (2006, background): “5), including in particular the linear case treated in [2], the non-standard p; q growth, the exponential growth considered in [21] and also the new example of oscillating function in (2.”
On the Regularity of Minima of Non-autonomous Functionals (2019, methodology): “tandard (p,q)-case when focusing on this situation (see Remark 6.2 below). The one (1.25)4 is known as µ-ellipticity condition and it is of common use in problems with linear and nearly-linear growth [6,9,27]. It has been introduced in [35]. Remark 1.3. The technique considered here can be modiﬁed u”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “Further developments can be found in [36] [241].”
Higher differentiability of minimizers of variational integrals with Sobolev coefficients (2012, unknown): “The regularity of minimizers of functionals satisfying (p, q) growth conditions has been widely investigated, both in the scalar and in the vectorial setting (see for example [1] [2] [3] [11] [12] [15] [16] [27] [28] [32]).”
Higher differentiability of minimizers of convex variational integrals (2011, unknown): “[2, 4, 7, 13, 14, 33, 34]).”
Partial Regularity for BV Minimizers (2018, background): “y,and it cannotwork for quasiconvexintegrands. Further referenceson various interesting aspects of existence and regularity of minimizers in the BV context with a standard convexityassumption include [12, 14, 15, 36]. Remark1.2. The mainpointof Theorem1.1is that thesmallness condition(1.8) underthe ”