Let Ω be a region of R N , N ≥ 2 with boundary ∂Ω. We say that ∂Ω is of class C 1 if ∀x 0 ∈ ∂Ω ∃ε > 0 such that within the ball B ε (x 0 ) ≡ {|xx 0 | < ε}, ∂Ω can be implicitly represented in a local system of coordinates as a level set of a function
$$\Phi \in {C^1}\left( {{B_\varepsilon }\left( {{x_0}} \right)} \right),\quad {\text{such}}\,{\text{that}}\left| {\nabla \Phi } \right| \ne 0\quad {\forall _x} \in {B_\varepsilon }\left( {{x_0}} \right).$$


Minkowski Inequality Physical Assumption Newton Force Lagrangian Path Ideal Compressible Fluid 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Emmanuele DiBenedetto
    • 1
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Dipartimento di IngegneriaIIa Università di Roma, Tor VergataRomeItaly

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