Struct SobolevSpaceData 

pub struct SobolevSpaceData {
    pub order: usize,
    pub p: f64,
    pub domain_dim: usize,
    pub domain: String,
}

Data for Sobolev space W^{k,p}(Ω).

Fields

order: usize

Differentiability order k.

p: f64

Integrability p (1 <= p <= ∞).

domain_dim: usize

Domain dimension n.

domain: String

Domain description.

Implementations

impl SobolevSpaceData

pub fn new(order: usize, p: f64, domain_dim: usize, domain: &str) -> Self

Creates Sobolev space data.

pub fn hilbert_sobolev(order: usize, domain_dim: usize, domain: &str) -> Self

Returns H^k = W^{k,2} Sobolev space.

pub fn embedding_exponent(&self) -> Option<f64>

Sobolev embedding: W^{k,p}(Ω) ↪ L^q(Ω) for 1/q = 1/p - k/n.

pub fn critical_sobolev_exponent(&self) -> Option<f64>

Returns the critical Sobolev exponent p* = np/(n-kp).

pub fn rellich_kondrachov_compact(&self) -> bool

Checks the Rellich-Kondrachov theorem (compact embedding).

pub fn trace_theorem(&self) -> String

Returns trace theorem statement.

Trait Implementations

impl Clone for SobolevSpaceData

fn clone(&self) -> SobolevSpaceData

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SobolevSpaceData

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.