Pustam | पुस्तम | পুস্তম🇳🇵<p>FUNDAMENTAL LEMMA OF THE CALCULUS OF VARIATIONS:<br>If a continuous multivariable function \(f\) on an open set \({\Omega\subset \mathbb {R} ^{d}}\) satisfies the equality <br>\[\displaystyle\int_\Omega\mathcal{f}(x)\mathcal{g}(x)\ \mathrm{d}x=0\] <br>for all compactly supported smooth functions \(g\) on \(\Omega\), then \(f\) is identically zero.<br><a href="https://mathstodon.xyz/tags/lemma" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>lemma</span></a> <a href="https://mathstodon.xyz/tags/calculusofvariations" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>calculusofvariations</span></a> <a href="https://mathstodon.xyz/tags/fundamentallemma" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamentallemma</span></a> <a href="https://mathstodon.xyz/tags/multivariablefunctions" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>multivariablefunctions</span></a> <a href="https://mathstodon.xyz/tags/calculus" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>calculus</span></a> <a href="https://mathstodon.xyz/tags/variations" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>variations</span></a> <a href="https://mathstodon.xyz/tags/functional" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>functional</span></a> <a href="https://mathstodon.xyz/tags/function" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>function</span></a> <a href="https://mathstodon.xyz/tags/smoothfunction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>smoothfunction</span></a> <a href="https://mathstodon.xyz/tags/analysis" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>analysis</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a></p>