For domains of class $C^{1,1}$, I know that the mean curvature of its boundary belongs to $L^{\infty}(\partial \Omega)$. Is $C^{1,1}$ regularity the least regularity needed for the mean curvature to be in $L^{\infty}(\partial \Omega)$? How about the conditions on the boundary of a domain to have bounded mean curvatures? Which references discusses this kind of topic?
2026-03-30 02:24:09.1774837449
Least regularity of boundary to have Lipschitz or bounded mean curvature?
22 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in PARTIAL-DIFFERENTIAL-EQUATIONS
- PDE Separation of Variables Generality
- Partial Derivative vs Total Derivative: Function depending Implicitly and Explicitly on Variable
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Harmonic Functions are Analytic Evan’s Proof
- If $A$ generates the $C_0$-semigroup $\{T_t;t\ge0\}$, then $Au=f \Rightarrow u=-\int_0^\infty T_t f dt$?
- Regular surfaces with boundary and $C^1$ domains
- How might we express a second order PDE as a system of first order PDE's?
- Inhomogeneous biharmonic equation on $\mathbb{R}^d$
- PDE: Determine the region above the $x$-axis for which there is a classical solution.
- Division in differential equations when the dividing function is equal to $0$
Related Questions in RIEMANNIAN-GEOMETRY
- What is the correct formula for the Ricci curvature of a warped manifold?
- How to show that extension of linear connection commutes with contraction.
- geodesic of infinite length without self-intersections
- Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold
- Geodesically convex neighborhoods
- The induced Riemannian metric is not smooth on the diagonal
- Intrinsic vs. Extrinsic notions of Harmonic maps.
- Equivalence of different "balls" in Riemannian manifold.
- Why is the index of a harmonic map finite?
- A closed manifold of negative Ricci curvature has no conformal vector fields
Related Questions in CURVATURE
- Sign of a curve
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- A closed manifold of negative Ricci curvature has no conformal vector fields
- CAT(0) references request
- Why is $\kappa$ for a vertical line in 2-space not undefined?
- Discrete points curvature analysis
- Local computation of the curvature form of a line bundle
- Closed surface embedded in $\mathbb R^3$ with nonnegative Gaussian curvature at countable number of points
- What properties of a curve fail to hold when it is not regular?
Related Questions in REGULARITY-THEORY-OF-PDES
- If $q>p$ then $H^q([0,2\pi])$ is dense in $H^p([0,2\pi])$>
- Motivation to define the boundary value
- 1-D Heat Equation, bounding difference in $\alpha$ given surface temperature
- Implications of weak convergence on the Lebesgue space to Sobolev space
- Harnack type Estimates for a p-Poisson equation with constant source term
- Regularity solution of the Poisson equation with mixed boundary condition
- Intuition for compact embedding of $H^1([0,1])$ in $L^2([0,1])$?
- Young's inequality with duality bracket
- laplace equation $L^p$ estimate
- Interior Gradient Estimate for the p-Elliptic equation
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?