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- W2129617850 abstract "We consider variational problems of splitting-type, i.e., we want to minimize $$ intlimits_{Omega}[f(widetilde{nabla} w)+g(partial_{n}w)],dx, $$ where $${widetilde{nabla}=(partial_{1},ldots,partial_{n-1})}$$ . Here f and g are two C 2-functions which satisfy power growth conditions with exponents 1 < p ≤ q < ∞. In the case p ≥ 2 there is a regularity theory for locally bounded minimizers $${u:mathbb{R}^nsupsetOmegarightarrowmathbb{R}^N}$$ without further restrictions on p and q if n = 2 or N = 1. In the subquadratic case the results are much weaker: we get C 1,α -regularity if we require q ≤ 2p + 2 for n = 2 or q < p + 2 for N = 1. In this paper, we show C 1,α -regularity under the bounds $${q<frac{2p+4}{2-p}}$$ resp. q < ∞." @default.
- W2129617850 created "2016-06-24" @default.
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- W2129617850 date "2010-04-17" @default.
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- W2129617850 title "A note on splitting-type variational problems with subquadratic growth" @default.
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- W2129617850 doi "https://doi.org/10.1007/s00013-010-0115-3" @default.
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