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Degenerate Parabolic and Elliptic Equations
1994The region where the equation deteriorates is fixed for linear and semilinear degenerate equations. The cases usually discussed are that the degenerate region is on the boundary. The two approaches are often used. One is the barrier argument and another is introducing the weighted Sobolev spaces.
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Degenerate Elliptic Equations and Boundary Problems
1994A differential operator A on a manifold Ω is called elliptic if its principal symbol A 0(x,ξ) does not vanish on T*0 (Ω) (see Egorov, Shubin 1988, Sect. 1). If Ω is a closed manifold and the order of the operator is m, then for any s ∈ ℝ1 it is a Fredholm H s+m(Ω) → H s(Ω) and the following a priori estimate holds: $${\left\| u \right\|_s}c(s)\left(
S. Z. Levendorskij, B. Paneah
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Solvability of degenerate quasilinear elliptic equations
Nonlinear Analysis: Theory, Methods & Applications, 1996The existence of weak solutions for degenerate elliptic boundary value problems is studied for the equation \[ - \sum^n_{i= 1} {\partial\over \partial x_i} a_i(x, u, \nabla u)+ \nu_0(x)|u|^{p- 2} u+ f(x, u, \nabla u)= 0.\tag{1} \] This equation is a generalization of equations of Klein-Gordon or Schrödinger type.
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Degenerate elliptic equations and sum operators
2020This Chapter is devoted to a new kind of degenerate elliptic operator. It is shown that it is possible to derive a regularity theory for this class. Despite the strong degeneracy of the operator, the smoothness of the generalized solutions can be proved.
Maria, Fanciullo +2 more
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Numerical evaluation of iterated integrals related to elliptic Feynman integrals
Computer Physics Communications, 2021Moritz Walden, Weinzierl Stefan
exaly
On Degenerating Elliptic Equations
Theory of Probability & Its Applications, 1969openaire +3 more sources
BIFURCATIONS IN DEGENERATE ELLIPTIC EQUATIONS
EQUADIFF 2003, 2005R. LAISTER, R. E. BEARDMORE
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A Liouville Theorem for Degenerate Elliptic Equations
Journal of the London Mathematical Society, 1973Edmunds, D. E., Peletier, L. A.
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