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Existence and regularity of solutions of elliptic PDE in $\mathbb{R}^n$

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#real-analysis #partial-differential-equations #calculus-of-variations #regularity-theory-of-pdes
319
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Existence of a Solution for a Nonlinear Heat Equation

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#partial-differential-equations #heat-equation #regularity-theory-of-pdes #parabolic-pde
52
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a query on compact embedding for critical exponent

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#functional-analysis #partial-differential-equations #regularity-theory-of-pdes
127
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Heat Equation with Initial Data in $L^1.$

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#partial-differential-equations #heat-equation #regularity-theory-of-pdes #greens-function #parabolic-pde
42
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Harnack for ball of radius $1/2$ imply Harnack for ball of any radius

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#functional-analysis #partial-differential-equations #regularity-theory-of-pdes
152
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Heat Equation with Measure as Initial Data

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#measure-theory #partial-differential-equations #heat-equation #geometric-measure-theory #regularity-theory-of-pdes
39
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Are Lipchitz isometries smooth up to the boundary?

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#riemannian-geometry #sobolev-spaces #isometry #regularity-theory-of-pdes #manifolds-with-boundary
66
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A priori estimates for almost similar similar pde's

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#partial-differential-equations #regularity-theory-of-pdes
164
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Regularity of solution of $u_t -\Delta u=f$ where $f$ is a continuous function

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#functional-analysis #partial-differential-equations #regularity-theory-of-pdes #parabolic-pde
99
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Hölder continuity of gradient

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#regularity-theory-of-pdes #elliptic-operators
91
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Solution theory for parabolic problems with irregular boundary data

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#partial-differential-equations #boundary-value-problem #regularity-theory-of-pdes
194
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Solving Poisson's equation on $B_1(0)\subset \mathbb{R}^2$

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#partial-differential-equations #regularity-theory-of-pdes #greens-function #poissons-equation
22
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Best regularity of free boundary problem modeled by laplacian

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#partial-differential-equations #boundary-value-problem #regularity-theory-of-pdes
31
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Examples of non-regular weak solutions for second order elliptic PDEs

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#partial-differential-equations #regularity-theory-of-pdes
39
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Conflicting answers on simiarly linear PDEs!$\;( u_{xxxx}+4u_{xy}=\tan{x} )$

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#partial-differential-equations #regularity-theory-of-pdes #linear-pde

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