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On the boundedness of generalized solutions of elliptic differential equations. (English. Russian original) Zbl 0548.35041
Russ. Math. Surv. 38, No. 2, 186-187 (1983); translation from Usp. Mat. Nauk 38, No. 2(230), 205-206 (1983).
It is shown that generalized solutions in \(\Omega\subset {\mathbb{R}}^ n\) of the partial differential equations \(div A(x,u,u_ x)=-f(x,u,u_ x)\) (with sufficient general hypothesis for A and f) are bounded: \( \sup_{\Omega}| u(x)|\leq M.\)
Reviewer: V.Olariu
MSC:
35J60 Nonlinear elliptic equations
35B35 Stability in context of PDEs
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