Abstract
In this chapter we establish a maximum principle type result that provides pointwise control on minimal solutions. In contrast to the usual maximum principle, it does not hold for solutions in general, not even for local minimizers in the scalar case. We obtain it as a corollary of a replacement lemma modeled after Lemmas 2.4 and 2.5.
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Alikakos, N.D., Fusco, G., Smyrnelis, P. (2018). The Cut-Off Lemma and a Maximum Principle. In: Elliptic Systems of Phase Transition Type. Progress in Nonlinear Differential Equations and Their Applications, vol 91. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-90572-3_4
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DOI: https://doi.org/10.1007/978-3-319-90572-3_4
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