Titlebook: A Compact Course on Linear PDEs; Alberto Valli Textbook 20201st edition The Editor(s) (if applicable) and The Author(s), under exclusive l

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Tsvi Kuflik,Shlomo Berkovsky,Antonio KrügerThis chapter is devoted to the solution of saddle point problems that can be written in the abstract form . for some linear operators . and ., . having the role of a Lagrangian multiplier associated to the constraint . = ..

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Tariq Muhammad,Julita VassilevaParabolic equations are equations of the form . where . is an elliptic operator, whose coefficients can depend on ..

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Efficiency Issues for Ultrasound,Hyperbolic equations have the form . where . is an elliptic operator, whose coefficients can depend on .. The “prototype” is the .. with speed . > 0.

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The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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https://doi.org/10.1007/978-981-10-1627-1ere, as done in Sects. . and ., we assume that . is a bounded, connected, open set, .. ∈ ..(.) for ., . = 1, …, ., .. ∈ ..(.) for . = 1, …, ., .. ∈ ..(.). When considering the Robin problem, the assumptions on the coefficient are . ∈ ..(.), . ≥ 0 a.e. on . and ∫... ≠ 0. On the data we assume that . 

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