What is the trick, to prove $\| u\|_{L^2(\Gamma)} \leq k \frac{1}{r}\| u\|_{L^2(\Omega)} + r \| \nabla u\|_{L^2(\Omega)} $ ? $\Gamma$ is one side of $\Omega:= [0,r] \times [0,r] $. I tried partial differentiation, but it doesnt work.
2026-04-02 06:22:25.1775110945
Some kind of trace inequality
186 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in INEQUALITY
- Confirmation of Proof: $\forall n \in \mathbb{N}, \ \pi (n) \geqslant \frac{\log n}{2\log 2}$
- Prove or disprove the following inequality
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
- Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.
- Solution to a hard inequality
- Is every finite descending sequence in [0,1] in convex hull of certain points?
- Bound for difference between arithmetic and geometric mean
- multiplying the integrands in an inequality of integrals with same limits
- How to prove that $\pi^{e^{\pi^e}}<e^{\pi^{e^{\pi}}}$
- Proving a small inequality
Related Questions in ESTIMATION
- Question on designing a state observer for discrete time system
- Some help with calculating the time remaining please???
- Is the usage of unbiased estimator appropriate?
- How to statistically estimate multiple linear coefficients?
- Is there an intuitive way to see that $\mathbb{E}[X|Y]$ is the least squares estimator of $X$ given $Y$?
- minimizing MSE of estimator $\theta(a,b) = \frac{1}{n} \sum^n_{i=1} Y_ia_i + b$
- a limit about exponential function
- I don't understand where does the $\frac{k-1}{k}$ factor come from, in the probability mass function derived by Bayesian approach.
- hints for calculation of double integral
- estimation of $\mu$ in a Gaussian with set confidence interval
Related Questions in TRACE
- How to show that extension of linear connection commutes with contraction.
- Basis-free proof of the fact that traceless linear maps are sums of commutators
- $\mathrm{tr}(AB)=\mathrm{tr}(BA)$ proof
- Similar 2x2 matrices of trace zero
- Basis of Image and kernel of Linear Transformation $\mathbb(M_{2,2})\rightarrow\mathbb(R^3) = (trace(A), 5*Trace(A), - Trace(A))$
- Replace $X$ with $\mbox{diag}(x)$ in trace matrix derivative identity
- Proving that a composition of bounded operator and trace class operator is trace class
- If $A \in \mathcal M_n(\mathbb C)$ is of finite order then $\vert \operatorname{tr}(A) \vert \le n$
- Characterisations of traces on $F(H)$
- "Symmetry of trace" passage in the proof of Chern Weil.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?