Boundary value problems are considered for quasilinear elliptic equations with a principal quasilinear elliptic operator of the second order in the Sobolev space $W_p^2 \left(\Omega\right)$. The main content of the work is to establish the maximum admissible growth of the subordinate nonlinear operator with respect to the corresponding lower-order derivatives. We consider a class of equations for which an a priori estimate of solutions in the norm of the space $\Vert u \Vert_{L_l \left( \Omega\right)}$ $\left( 1 \leq l < \infty \right)$ implies an a priori estimate of the solution in the norm of the space $W_p^2 \left(\Omega\right)$. Based on the theorem on a priori estimates, a general solvability theorem for boundary value problems for quasi-linear elliptic equations is obtained under the condition of the existence of an intermediate a priori estimate $\Vert u \Vert_{L_l \left( \Omega\right)}$ for the solutions of the corresponding family of boundary value problems.
| Mualliflar | Amanova, N. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-07-02 |
| Jild | 70 |
| Son | 2 |
| Betlar | 24-32 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-2-3 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-2-3 · Maqolaning asl sahifasi
interpolation method, Sobolev space, quasilinear equation
| APA | Amanova, N. (2026). On some existence theorems for quasilinear elliptic equations. O‘zbekiston matematika jurnali, 70(2), 24-32. https://doi.org/10.29229/uzmj.2026-2-3 |
|---|---|
| GOST (OAK) | Amanova, N. On some existence theorems for quasilinear elliptic equations // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 2. – P. 24-32. – DOI: 10.29229/uzmj.2026-2-3. |
| MLA | Amanova, N. “On some existence theorems for quasilinear elliptic equations.” O‘zbekiston matematika jurnali, 70(2), 24-32, 2026. https://doi.org/10.29229/uzmj.2026-2-3 |
| Chicago | Amanova, N. “On some existence theorems for quasilinear elliptic equations.” O‘zbekiston matematika jurnali, 70(2), 24-32 (2026). https://doi.org/10.29229/uzmj.2026-2-3 |
| Harvard | Amanova, N (2026) ‘On some existence theorems for quasilinear elliptic equations’, O‘zbekiston matematika jurnali, 70(2), 24-32. https://doi.org/10.29229/uzmj.2026-2-3 |
| BibTeX | @article{amanovan2026,
title = {On some existence theorems for quasilinear elliptic equations},
author = {Amanova, N.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {2},
pages = {24-32},
doi = {10.29229/uzmj.2026-2-3},
url = {https://doi.org/10.29229/uzmj.2026-2-3}
} |
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