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Lp-estimates for a transmission problem of mixed elliptic-parabolic type
2014
Boundary Value Problems
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We consider the situation when an elliptic problem in a subdomain 1 of an n-dimensional bounded domain is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in \ 1 . In particular, we can treat elliptic-parabolic equations in bounded domains with discontinuous coefficients. Using Fourier multiplier techniques, we prove an a priori estimate for strong solutions to the equations in L p -Sobolev spaces. MSC: 35B45; 35M12
doi:10.1186/1687-2770-2014-22
fatcat:ogml6aj2pbgvhny7god5oa5x2a