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1
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Exact Schauder estimates of solutions of a boundary value problem for parabolic second order equations and their application to a nonlinear problem

100%
Borsuk M.
Annales Polonici Mathematici
|
2002
|
tom 79
|
nr 3
207-232
EN
We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.
2
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Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

100%
Borsuk M.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 2
129-154
EN
We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives.
3
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Best possible estimates of solutions to the transmission problem for the Laplace operator with N different media in a conical domain

100%
Borsuk M.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 4
445-491
EN
We investigate the behavior of weak solutions to the transmission problem for the Laplace operator with N different media in a neighborhood of a boundary conical point. We establish a precise exponent of the decreasing rate of the solution.
4
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Nonlocal Robin problem for elliptic second order equations in a plane domain with a boundary corner point

64%
Borsuk M., Żyjewski K.
Applicationes Mathematicae
|
2011
|
tom 38
|
nr 4
369-411
EN
We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.
5
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Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains

64%
Borsuk M., Wiśniewski D.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2051-2072
EN
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.
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