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Zbl 0969.35057
Fattorusso, L.; Idone, G.
Partial Hölder continuity results for solutions of nonlinear non variational elliptic systems with strictly controlled growth. (English)
[J] Rend. Semin. Mat. Univ. Padova 103, 1-19 (2000). ISSN 0041-8994

The authors study partial regularity results for strong solutions $u\in H^2(\Omega, \bbfR^N)$ of the fully nonlinear nonvariational system $a(x, u,Du,D^2u)= b(x,uDu)$, $x\in \Omega$. Here, $\Omega\subset \bbfR^n$, $n> 4$, is a bounded open set, $a$, $b$ are $\bbfR^N$-valued functions. A number of technical conditions are imposed on $a$ and $b$, the most important of which may be summarized as follows: An ellipticity condition on $a$, which further implies linear growth w.r.t $D^2u$ and that the linearization of $u$ deviates not too much from the Laplace operator. Measurability w.r.t $x$, continuity w.r.t $u$ and $Du$ and continuous differentiability w.r.t $D^2u$. For the lower-order term $b$, subcritical growth (w.r.t to the linear growth of $a)$ and the solution class $H^2$ is assumed. Under these conditions, Hölder regularity of $Du$ is shown, possibly except on a set of measure $0$.\par Related results can be found in [{\it S. Campanato}, Rend. Mat. Appl., VII. Ser. 10, No. 3, 531-549 (1990; Zbl 0777.35028)].
[Hans-Christoph Grunau (Bayreuth)]

MSC 2000:: *35J60 Nonlinear elliptic equations
35D10 Regularity of generalized solutions of PDE
35J45 Systems of elliptic equations, general
35B65 Smoothness of solutions of PDE

Keywords: partial regularity; fully nonlinear elliptic systems

Citations: Zbl 0777.35028

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