scholarly journals Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

1998 ◽  
Vol 69 (2) ◽  
pp. 129-154 ◽  
Author(s):  
Michail Borsuk
Keyword(s):  
Dirichlet Problem ◽  
Second Order ◽  
Generalized Solutions ◽  
Nonsmooth Domains ◽  
Derivatives Of ◽  
Second Order Equations

scholarly journals Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

2017 ◽  
Vol 15 (1) ◽  
pp. 768-786
Author(s):  
Yuliya Gorban
Keyword(s):  
Dirichlet Problem ◽  
Present Article ◽  
Unknown Function ◽  
Entropy Solutions ◽  
Independent Variables ◽  
Nonlinear Elliptic ◽  
Weighted Functions ◽  
Rates Of Growth ◽  
Derivatives Of ◽  
Second Order Equations

Abstract In the present article we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L1-right-hand sides in a bounded domain of ℝn(n ⩾ 2) . This class is described by the presence of a set of exponents q1,…, qn and a set of weighted functions ν1,…, νn in growth and coercitivity conditions on coefficients of the equations. The exponents qi characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions νi characterize degeneration or singularity of the coefficients with respect to independent variables. Our aim is to investigate the existence of entropy solutions of the problem under consideration.

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