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Hidden regularity for semilinear hyperbolic partial differential equations. (English) Zbl 0618.35073
Hidden regularity is a concept introduced by J. L. Lions for the nonlinear wave equation \(u_{tt}-\Delta u+| u| ^{\rho}u=0\). The authors prove the same type of regularity for the equation \(u_{tt}- \Delta u+F(u)=0\) under the hypothesis of W. A. Strauss, i.e., \(F: {\mathbb{R}}\to {\mathbb{R}}\) is continuous and sF(s)\(\geq 0\). In § 3 the authors develop certain notions about the trace of the normal derivative.

MSC:
35L70 Second-order nonlinear hyperbolic equations
35B65 Smoothness and regularity of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:
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