The structure of a strongly degenerate differential equation with holomorphic coefficients

1996 ◽  
Vol 36 (2) ◽  
pp. 131-141
Author(s):  
B. Kvedaras
Keyword(s):  
Differential Equation ◽  
Degenerate Differential Equation ◽  
Strongly Degenerate

CONDITIONS OF EXISTENCE THE TRACE OF FUNCTIONS FROM SPACE WITH MULTIWEIGHTED DERIVATIVES IN A SPECIAL POINT

2020 ◽  
pp. 123-128
Author(s):  
А. Kalybay ◽  
◽  
Zh. Keulimzhaeva ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Space ◽  
Variable Coefficients ◽  
Weight Functions ◽  
Weight Sobolev Space ◽  
Strongly Degenerate

When solving differential equations with variable coefficients, especially when the coefficients degenerate at the boundary of a given domain, problems arise in the formulation of boundary value problems. Usually, differential equations with variable coefficients are investigated in a suitable weight functional space. Often in the role of such spaces the weight Sobolev space or various generalizations are considered, which are currently sufficiently studied. However, in some cases, when the coefficients of the considered differential equation are strongly degenerate, the formulation of boundary value problems becomes problematic. In this work, we consider the so-called space with multiweighted derivatives, where after each derivative, the function is multiplied by the weight function and then the next derivative is taken. By controlling the behavior of the weight functions on the boundary, strongly degenerate equations can be investigated. Here we investigate the existence of traces on the boundary of a function from such spaces.

scholarly journals Optimal time and space regularity for solutions of degenerate differential equations

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Alberto Favaron
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Cauchy Problem ◽  
Differential Equations ◽  
Optimal Time ◽  
Time And Space ◽  
Optimal Regularity ◽  
Degenerate Differential Equation ◽  
The Cauchy Problem ◽  
Degenerate Differential Equations

AbstractWe derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.

SOME RESULTS ON PARTIAL DIFFERENTIAL EQUATIONS AND ASIAN OPTIONS

2001 ◽  
Vol 11 (03) ◽  
pp. 475-497 ◽  
Author(s):  
E. BARUCCI ◽  
S. POLIDORO ◽  
V. VESPRI
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Three Dimensions ◽  
Asian Options ◽  
Partial Differential ◽  
No Arbitrage ◽  
Strongly Degenerate ◽  
Degenerate Partial Differential Equations

We analyze partial differential equations arising in the evaluation of Asian options. The equations are strongly degenerate partial differential equations in three dimensions. We show that the solution of the no-arbitrage partial differential equation is sufficiently regular and standard numerical methods can be employed to approximate it.

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