Geodesic
Remarks on the Uniqueness of a Solution of the Dirichlet Problem for Second-Order Elliptic Equations with Lower-Order Terms
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 3, pp. 15-28

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We give an example of an incompressible diffusion equation whose solution is nonunique. It is shown that this equation has an approximation solution as well as another solution that cannot be obtained by approximation. We give sufficient conditions for the uniqueness of a solution as well as for the uniqueness of an approximation solution.
Keywords: approximation solution, nonuniqueness, energy identity, maximal function, higher integrability. 
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     author = {V. V. Zhikov},
     title = {Remarks on the {Uniqueness} of a {Solution} of the {Dirichlet} {Problem} for {Second-Order} {Elliptic} {Equations} with {Lower-Order} {Terms}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {15--28},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_3_a1/}
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V. V. Zhikov. Remarks on the Uniqueness of a Solution of the Dirichlet Problem for Second-Order Elliptic Equations with Lower-Order Terms. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 3, pp. 15-28. http://geodesic.mathdoc.fr/item/FAA_2004_38_3_a1/