Zusammenfassung
Wir beginnen mit einer elementaren Beobachtung: Es sei\( \begin{array}{*{20}{c}} {\left\| {{D^2}v} \right\|_{{L^2}(\Omega )}^2 = \int_\Omega {\sum\limits_{i,j = 1}^d {{v_{{x^i}{x^j}}}{v_{{x^i}{x^j}}}} } } \\ { = - \int_\Omega {\sum\limits_{i,j = 1}^d {{v_{{x^i}{x^j}{x^i}}}{v_{{x^j}}}} } } \\ { = \int_\Omega {\sum\limits_{i = 1}^d {{v_{{x^i}{x^i}}}} \sum\limits_{j = 1}^d {{v_{{x^j}{x^j}}}} } } \\ { = \left\| {\Delta v} \right\|_{{L^2}(\Omega )}^2} \end{array}\) .
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© 1998 Springer-Verlag Berlin Heidelberg
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Jost, J. (1998). Starke Lösungen. In: Partielle Differentialgleichungen. Springer-Lehrbuch Masterclass. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58888-4_10
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DOI: https://doi.org/10.1007/978-3-642-58888-4_10
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