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Regularity for minima of functionals with p-growth. (English) Zbl 0674.35008
We prove that the first derivatives of scalar minima of functionals of the type \[ I(u)=\int f(x,u,\nabla u)dx, \] are Hölder continuous. Here \(f(x,u,\nabla u)\approx | \nabla u|^ p,\) \(1<p<\infty\) and f is assumed Hölder continuous in x and u.
We give two applications. One to the regularity theory of quasiregular mappings and the other to quasilinear degenerate elliptic equations with p-growth.
Reviewer: J.J.Manfredi

MSC:
35B65 Smoothness and regularity of solutions to PDEs
35J70 Degenerate elliptic equations
35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A15 Variational methods applied to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
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