| Title | The Dirichlet problem for the Poisson type equations in the plane |
| Publication Type | Journal Article |
| Year of Publication | 2020 |
| Authors | Gutlyanskii, VYa., Nesmelova, OV, Ryazanov, VI |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2020.05.010 |
| Issue | 5 |
| Section | Mathematics |
| Pagination | 10-16 |
| Date Published | 5/2020 |
| Language | English |
| Abstract | We present a new approach to the study of semilinear equations of the form div [A(z)∇u] = f (u), the diffusion term of which is the divergence uniform elliptic operator with measurable matrix functions A(z), whereas its reaction term f (u) is a continuous non-linear function. We establish a theorem on the existence of weak C(D)∩W1.2loc (D) solutions of the Dirichlet problem with arbitrary continuous boundary data in any bounded domains D without degenerate boundary components and give applications to equations of mathematical physics in anisotropic media. |
| Keywords | anisotropic and inho mogeneous media, Dirichlet problem, quasiconformal maps, quasilinear Poisson equations, semilinear elliptic equations |
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