Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces

From MaRDI portal

Publication:1132280

Jump to:navigation, search

DOI10.1007/BF02411942zbMath0419.35041OpenAlexW2028484035MaRDI QIDQ1132280

Giorgio Talenti

Publication date: 1979

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02411942

zbMATH Keywords

weak solution a priori estimates boundary value problem Orlicz spaces nonlinear elliptic equations rearrangements of functions

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Nonlinear boundary value problems for linear elliptic equations (35J65) A priori estimates in context of PDEs (35B45)

Related Items

A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions ⋮ A limiting regularity result for some parabolic problems with data in Zygmund spaces ⋮ Symmetrization for fractional nonlinear elliptic problems ⋮ Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds ⋮ A global second-order Sobolev regularity for \(p\)-Laplacian type equations with variable coefficients in bounded domains ⋮ A strongly nonlinear elliptic problem with generalized growth in Musielak spaces ⋮ On eigenvalue problems involving the critical Hardy potential and Sobolev type inequalities with logarithmic weights in two dimensions ⋮ Existence and comparison results for quasilinear elliptic equations with critical growth in the gradient ⋮ Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application ⋮ Quasilinear problems with singularities ⋮ Long-time behaviour of the solution to the Cauchy problem for degenerate parabolic equations with nonpower nonlinearities ⋮ On concavity of solutions of the nonlinear Poisson equation ⋮ Asymptotic behaviour of a semilinear elliptic system with a large exponent ⋮ Optimal summability of solutions to nonlinear elliptic problems ⋮ Parabolic inequalities in Orlicz spaces with data in \(L^1\) ⋮ Symmetrization in Anisotropic Elliptic Problems ⋮ Nonlinear elliptic equations with measure data ⋮ Comparison results for solutions to \(p\)-Laplace equations with Robin boundary conditions ⋮ Natural second-order regularity for parabolic systems with operators having \((p, \delta)\)-structure and depending only on the symmetric gradient ⋮ Anisotropic elliptic equations with general growth in the gradient and Hardy-type potentials ⋮ Convex symmetrization and applications ⋮ Rearrangement minimization problems with indefinite external forces ⋮ The \(p\)-harmonic system with measure-valued right hand side ⋮ Ergodic problem for optimal stochastic switching ⋮ Estimates for solutions of nonlinear variational inequalities ⋮ A pocket guide to nonlinear differential equations in Musielak-Orlicz spaces ⋮ Symmetrization in a nonlinear degenerate parabolic problem ⋮ The biharmonic Alt-Caffarelli problem in 2D ⋮ Dirichlet problem for elliptic equations with nonlinear first order terms: a comparison result ⋮ A pointwise differential inequality and second-order regularity for nonlinear elliptic systems ⋮ Sharp Sobolev type embeddings on the entire Euclidean space ⋮ \(L^ \infty\)-solutions for some nonlinear degenerate elliptic and parabolic equations ⋮ Estimates for generalized subsolutions of first order Hamilton-Jacobi equations and rearrangements ⋮ Symmetrization for fractional elliptic problems: a direct approach ⋮ A symmetrization result for a class of anisotropic elliptic problems ⋮ Quasilinear elliptic problems with general growth and merely integrable, or measure, data ⋮ Schwarz symmetrization and comparison results for nonlinear elliptic equations and eigenvalue problems ⋮ On elliptic equations in Orlicz spaces involving natural growth term and measure data ⋮ On some nonlinear degenerate elliptic equations having a lower term in Musielak spaces ⋮ Elliptic equations on manifolds and isoperimetric inequalities ⋮ On the Caffarelli-Kohn-Nirenberg-type inequalities involving critical and supercritical weights ⋮ Estimates for fully anisotropic elliptic equations with a zero order term ⋮ Estimates for solutions to nonlinear degenerate elliptic equations with lower order terms ⋮ Comparison results for solutions of elliptic Neumann problems with lower-order terms via Steiner symmetrization ⋮ Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces ⋮ Bang-Bang and Multiple Valued Optimal Solutions of Control Problems Related to Quasi-linear Elliptic Equations ⋮ Some stability estimates for the symmetrized first eigenfunction of certain elliptic operators ⋮ Talenti's comparison theorem for Poisson equation and applications on Riemannian manifold with nonnegative Ricci curvature ⋮ A rigidity result for the Robin torsion problem ⋮ Solutions for nonlinear elliptic equations with variable growth and degenerate coercivity ⋮ On the first eigenvalue of the clamped plate ⋮ Convex symmetrization and Pólya--Szegö inequality. ⋮ Nonlinear elliptic and parabolic equations involving measure data ⋮ Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type ⋮ Unnamed Item ⋮ Regularity results for solutions of nonlinear elliptic equations with \(L^{1,\lambda }\) data ⋮ Regularity results for the gradient of solutions linear elliptic equations with \(L^{1,\lambda}\) data ⋮ Continuous dependence on the data for nonlinear elliptic equations with a lower order term ⋮ Symmetrization inequalities ⋮ Optimal estimates for fractional fast diffusion equations ⋮ A priori estimates for elliptic equations with gradient dependent term and zero order term ⋮ Combination and mean width rearrangements of solutions to elliptic equations in convex sets ⋮ Gradient estimates via rearrangements for solutions of some Schrödinger equations ⋮ Comparison results for solutions to the anisotropic Laplacian with Robin boundary conditions ⋮ The elastic flow with obstacles: small obstacle results ⋮ Comparison estimates in anisotropic variational problems ⋮ An embedding theorem in Lorentz-Zygmund spaces ⋮ Neumann problems and isocapacitary inequalities ⋮ Global boundedness of the gradient for a class of Schrödinger equations ⋮ Comparison results and improved quantified inequalities for semilinear elliptic equations ⋮ Optimal existence and uniqueness theory for the fractional heat equation ⋮ Existence results for some nonlinear elliptic equations with measure data in Orlicz-Sobolev spaces ⋮ Symmetrization results for classes of nonlinear elliptic equations with q-growth in the gradient ⋮ Missing terms in Hardy-Sobolev inequalities ⋮ On the Faber–Krahn inequality for the Dirichletp-Laplacian ⋮ Existence and comparison results for non-uniformly parabolic problems ⋮ New isoperimetric estimates for solutions to Monge-Ampère equations ⋮ Pointwise symmetrization inequalities for Sobolev functions and applications ⋮ Comparison and Existence Results for Classes of Nonlinear Elliptic Equations with General Growth in the Gradient ⋮ Well-posed elliptic Neumann problems involving irregular data and domains ⋮ Nonlinear elliptic problems having natural growth and \(L^1\) data in Orlicz spaces ⋮ \(L^\infty\)-bounds of solutions for a class of strongly nonlinear elliptic equations in Musielak spaces ⋮ Second-order two-sided estimates in nonlinear elliptic problems ⋮ On the Caffarelli-Kohn-Niremberg type inequalities and related topics ⋮ New Pólya-Szegö-type inequalities and an alternative approach to comparison results for PDE's ⋮ Comparison and regularity results for a nonlinear elliptic equation ⋮ Unnamed Item ⋮ Optimization problems for an energy functional with mass constraint revisited ⋮ Measure-valued solutions and the phenomenon of blow-down in logarithmic diffusion ⋮ A Talenti-type comparison theorem for \(\mathrm{RCD}(K,N)\) spaces and applications ⋮ Elliptic equations, rearrangements, and functions of bounded lower oscillation ⋮ A proof of the Faber-Krahn inequality for the first eigenvalue of the \(p\)-Laplacian ⋮ Optimal domain spaces in Orlicz-Sobolev embeddings ⋮ An existence result for nonlinear and noncoercive problems ⋮ A Priori Estimates and Comparison Principle for Some Nonlinear Elliptic Equations ⋮ Fully anisotropic elliptic problems with minimally integrable data ⋮ Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations ⋮ Estimates for the gradient of solutions of nonlinear elliptic equations with \(L^1\) data ⋮ Gradient estimates and comparison principle for some nonlinear elliptic equations ⋮ Rearrangement in variational inequalities ⋮ An optimization problem in thermal insulation with Robin boundary conditions ⋮ Comparison results for Poisson equation with mixed boundary condition on manifolds ⋮ Controlling monotonicity of nonlinear operators ⋮ Analysis and numerical studies of a problem of shape design ⋮ Global gradient estimates in elliptic problems under minimal data and domain regularity ⋮ Large solutions for the elliptic 1-Laplacian with absorption ⋮ Asymptotic Estimates for the Parabolic-Elliptic Keller-Segel Model in the Plane ⋮ Sharp a priori estimates for a class of nonlinear elliptic equations with lower order terms

Cites Work

This page was built for publication: Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1132280&oldid=29966674"