Concept

Gårding's inequality

Summary
In mathematics, Gårding's inequality is a result that gives a lower bound for the bilinear form induced by a real linear elliptic partial differential operator. The inequality is named after Lars Gårding. Statement of the inequality Let \Omega be a bounded, open domain in n-dimensional Euclidean space and let H^k(\Omega) denote the Sobolev space of k-times weakly differentiable functions u\colon\Omega\rightarrow\mathbb{R} with weak derivatives in L^2(\Omega). Assume that \Omega satisfies the k-extension property, i.e., that there exists a bounded linear operator E\colon H^k(\Omega)\rightarrow H^k(\mathbb{R}^n) such that Eu\vert_\Omega=u for all u\in H^k(\Omega). Let L be a linear partial differential operator of even order 2k, written in divergence form :(L u)(x) = \sum_{0 \leq | \alpha |, | \beta | \leq k} (-1)^{| \alpha |} \
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading