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A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces.(English)Zbl 1113.35062

Summary: We present a new general method to obtain regularity and a priori estimates for solutions of semilinear elliptic systems in bounded domains. This method is based on a bootstrap procedure, used alternatively on each component, in the scale of weighted Lebesgue spaces \(L^p_\delta(\Omega)=L^p(\Omega\delta(x)\,dx)\), where \(\delta(x)\) is the distance to the boundary. Using this method, we significantly improve the known existence results for various classes of elliptic systems.

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J50 Variational methods for elliptic systems
35J60 Nonlinear elliptic equations

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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