ON THE CONNECTION BETWEEN TWO QUASILINEAR ELLIPTIC PROBLEMS WITH SOURCE TERMS OF ORDER 0 OR 1
From MaRDI portal
Publication:3056466
DOI10.1142/S0219199710003993zbMath1205.35135arXiv0811.3292MaRDI QIDQ3056466
Unnamed Author, Haydar Abdel Hamid
Publication date: 12 November 2010
Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0811.3292
regularityDirichlet problemexistencemultiplicityuniquenessquasilinear elliptic equationsextremal solutionsmeasure data
Smoothness and regularity of solutions to PDEs (35B65) Weak solutions to PDEs (35D30) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Quasilinear elliptic equations (35J62) Quasilinear elliptic equations with (p)-Laplacian (35J92)
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Cites Work
- Unnamed Item
- Unnamed Item
- Approximated solutions of equations with \(L^ 1\) data. Application to the \(H\)-convergence of quasilinear parabolic equations
- Some remarks on elliptic problems with critical growth in the gradient
- Simplicity of principal eigenvalue for \(p\)-Laplace operator with singular indefinite weight
- Boundedness of the extremal solution of some \(p\)-Laplacian problems
- Nonlinear elliptic and parabolic equations involving measure data
- A general mountain pass principle for locating and classifying critical points
- Maximal regularity via reverse Hölder inequalities for elliptic systems of \(n\)-Laplace type involving measures
- Quasilinear elliptic equations with signed measure
- Regularity of radial minimizers of reaction equations involving the \(p\)-Laplacian
- Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
- Combined effects of concave and convex nonlinearities in some elliptic problems
- Inverting the \(p\)-harmonic operator
- Blow-up for two nonlinear problems
- Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small
- Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term.
- \(L^r\) estimates for degenerate elliptic problems
- Existence results for semilinear elliptic equations with small measure data
- Parabolic capacity and soft measures for nonlinear equations
- Regularity of the extremal solution of some nonlinear elliptic problems involving the \(p\)-Laplacian
- Nonlinear elliptic equations having a gradient term with natural growth
- Estimates for the gradient of solutions of nonlinear elliptic equations with \(L^1\) data
- Existence results for nonlinear elliptic equations with degenerate coercivity
- BOUNDEDNESS OF THE EXTREMAL SOLUTION FOR SEMILINEAR ELLIPTIC PROBLEMS
- Quasilinear elliptic equations involving critical Sobolev exponents
- Sur une classe de problemes non lineaires avec non linearite positive, croissante, convexe.
- On an Emden-Fowler type equation
- Bounded Palais-Smale mountain-pass sequences
- A Picone's identity for the p-Laplacian and applications
- Quasilinear problems with exponential growth in the reaction term
- Regularity of the extremal solution of semilinear elliptic equations
- A Local estimate for nonlinear equations with discontinuous coefficients
- STABILITY PROPERTIES, EXISTENCE, AND NONEXISTENCE OF RENORMALIZED SOLUTIONS FOR ELLIPTIC EQUATIONS WITH MEASURE DATA1*
- Nonexistence results and estimates for some nonlinear elliptic problems