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Partial regularity of the minimizers of quadratic functionals with VMO coefficients. (English) Zbl 1161.35347
Summary: The paper investigates the partial regularity of the minimizers for quadratic functionals whose integrands have VMO coefficients in principal part and nonlinear terms that are Carathéodory functions. We use some majorizations for the functional, rather than the well known Euler equation associated to it.

MSC:
35J10 Schrödinger operator, Schrödinger equation
35B65 Smoothness and regularity of solutions to PDEs
35N10 Overdetermined systems of PDEs with variable coefficients
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
35R05 PDEs with low regular coefficients and/or low regular data
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