We prove the higher differentiability and the higher integrability of the a priori bounded local minimizers of integral functionals of the form F(v,Ω)=∫ Ω f(x,Dv(x))dx, with convex integrand satisfying p-growth conditions with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the x-variable belongs to a suitable Sobolev space. The a priori boundedness of the minimizers allows us to obtain the higher differentiability under a Sobolev assumption which is independent on the dimension n and that, in the case p≤n−2 , improves previous known results. We also deal with solutions of elliptic systems with discontinuous coefficients under the so-called Uhlenbeck structure. In this case, it is well known that the solutions are locally bounded and therefore we obtain analogous regularity results without the a priori boundedness assumption

Regularity results for a priori bounded minimizers of non-autonomous functionals with discontinuous coefficients

GIOVA, Raffaella;
2019

Abstract

We prove the higher differentiability and the higher integrability of the a priori bounded local minimizers of integral functionals of the form F(v,Ω)=∫ Ω f(x,Dv(x))dx, with convex integrand satisfying p-growth conditions with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the x-variable belongs to a suitable Sobolev space. The a priori boundedness of the minimizers allows us to obtain the higher differentiability under a Sobolev assumption which is independent on the dimension n and that, in the case p≤n−2 , improves previous known results. We also deal with solutions of elliptic systems with discontinuous coefficients under the so-called Uhlenbeck structure. In this case, it is well known that the solutions are locally bounded and therefore we obtain analogous regularity results without the a priori boundedness assumption
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/63175
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