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1998
It is shown that under appropriate ellipticity assumptions, weak solutions of partial differential equations (PDEs) are smooth. This applies in particular to the Laplace equation for harmonic functions, thereby justifying Dirichlet’s principle introduced in the previous paragraph.
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It is shown that under appropriate ellipticity assumptions, weak solutions of partial differential equations (PDEs) are smooth. This applies in particular to the Laplace equation for harmonic functions, thereby justifying Dirichlet’s principle introduced in the previous paragraph.
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Weak Solutions for Hyperbolic Equations
2018In principle, in this chapter, we will study the wave equation, which constitutes the prototype of the hyperbolic equations. Let \(\Omega \) be an open set from \(\mathrm{I}\!\mathrm{R}^n\) and T a real number \(T>0\). Then, the Cauchy problem, associated with the wave equation, consists of $$\begin{aligned}&\frac{\partial ^2u}{\partial t^2}(t,x)- \
Marin Marin, Andreas Öchsner
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Weak solutions of the time-fractional Navier–Stokes equations and optimal control
Computers and Mathematics With Applications, 2017Yong Zhou, Li Peng
exaly
Global weak solutions and blow-up structure for the Degasperis–Procesi equation
Journal of Functional Analysis, 2006Joachim Escher, Zhaoyang Yin
exaly